10th Class Mathematics Triangles Question Bank

done Triangles Total Questions - 30

• question_answer1)
  A \[\Delta \,PQR\] inscribes a circle as shown. Let points of tangency be L, M, N. If PQ = 6 inch, QR = 8 inc, RP = 10 inch, then PL + QM + RN =­­­­­­­­­­­­___________
  A)
   24 inch                         done clear
  B)
   30 inch                       done clear
  C)
   15 inch                         done clear
  D)
   12 inch    done clear
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• question_answer2)
                 In figure, \[\Delta \,ODC\sim \Delta \,OBA,\angle BOC=125{}^\circ \] and\[\angle \,CDO=70{}^\circ \]. Find\[\angle OAB\]
  A)
   \[65{}^\circ \]                          done clear
  B)
   \[55{}^\circ \]  done clear
  C)
   75                                done clear
  D)
   \[45{}^\circ \]         done clear
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• question_answer3)
                                            Diagonals AC and BD of a trapezium ABCD with \[AB\parallel DC\]intersect each other the point O. Then:
  A)
   \[\frac{OA}{OC}=\frac{OB}{OD}\]       done clear
  B)
   \[\frac{AB}{OC}=\frac{OA}{OC}\] done clear
  C)
   \[\angle OAB=\angle ODC\]        done clear
  D)
   \[\frac{OA}{OB}=\frac{OC}{OD}\] done clear
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• question_answer4)
  Find the value of 'x' from the figure given below if\[EF\parallel BC\].
  A)
   3                                 done clear
  B)
   2.5                                             done clear
  C)
   1.5                               done clear
  D)
   1 done clear
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• question_answer5)
  In a triangular field PQR, MN is parallel to the side QR. If PM = 56m, PQ = 70m and MN = 30m, then find QR.
  A)
   37.5 m       done clear
  B)
   40 m             done clear
  C)
   42.5 m                         done clear
  D)
   45 m done clear
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• question_answer6)
  In an equilateral triangle the length of the altitude is 16 cm,  then find the area of triangle,
  A)
   \[256c{{m}^{2}}\]                              done clear
  B)
   \[96\sqrt{3}c{{m}^{2}}\] done clear
  C)
   \[\frac{66}{\sqrt{3}}c{{m}^{2}}\]                   done clear
  D)
   \[\frac{256}{\sqrt{3}}c{{m}^{2}}\] done clear
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• question_answer7)
  Find the value of x from the figure given below, if\[ST\parallel QR\]
  A)
   1.5                               done clear
  B)
   3.2 done clear
  C)
   1         done clear
  D)
   5 done clear
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• question_answer8)
  Look at the figure where \[\Delta PQR\]is congruent to \[\Delta \,SRQ\](note the order of letters for congruency).  \[PQ\times SQ\]equals.............(fill in the blanks)
  A)
   \[PR\times SR\]  done clear
  B)
   \[OP\times OQ\] done clear
  C)
   \[PQ\times OP\]             done clear
  D)
   \[OP\times OR\] done clear
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• question_answer9)
  In rhombus\[PQRS,P{{Q}^{2}}+Q{{R}^{2}}+R{{S}^{2}}+S{{P}^{2}}=\].....
  A)
   \[P{{R}^{2}}+S{{Q}^{2}}\]             done clear
  B)
   \[O{{S}^{2}}+P{{R}^{2}}\]      done clear
  C)
   \[O{{R}^{2}}+O{{S}^{2}}\]                        done clear
  D)
   \[O{{P}^{2}}+O{{R}^{2}}\]          done clear
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• question_answer10)
  Sides of two similar \[{{\Delta }^{s}}\] in the ratio\[2:3\]. Areas of these triangles are in the ratio
  A)
   2:3                               done clear
  B)
   \[4:9\]   done clear
  C)
   \[16:25\]                       done clear
  D)
   \[20:44\] done clear
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• question_answer11)
  In given figure, O is a point in the interior of a\[\Delta \,ABCD\], \[OD\bot BC,\text{ }OE\bot AC\] and \[OF\bot AB\]. Then:                         
  A)
   \[O{{A}^{2}}+O{{B}^{2}}+O{{C}^{2}}-O{{D}^{2}}-O{{E}^{2}}-O{{F}^{2}}\]\[=A{{F}^{2}}+B{{D}^{2}}+C{{E}^{2}}\]   done clear
  B)
  \[A{{F}^{2}}+B{{D}^{2}}+C{{E}^{2}}=A{{E}^{2}}+C{{D}^{2}}\]                         done clear
  C)
   \[O{{A}^{2}}+O{{B}^{2}}+O{{D}^{2}}=O{{E}^{2}}+O{{F}^{2}}+O{{C}^{2}}\]                done clear
  D)
  \[A{{F}^{2}}+A{{E}^{2}}=B{{D}^{2}}+C{{D}^{2}}\] done clear
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• question_answer12)
                                     A ladder 2.6 metres long reaches a window 2.4 metres above the ground. Find the distance at which the foot of the ladder lies away from wall.
  A)
   1.6 metres         done clear
  B)
   1.2 metres          done clear
  C)
   0.6 metres                     done clear
  D)
   1 metre done clear
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• question_answer13)
  Given in the figure\[\angle QPR\text{ }=\angle PMR\], then \[\frac{RP}{RQ}=\]??.
  A)
   \[P{{Q}^{2}}\]                       done clear
  B)
   \[P{{R}^{3/2}}\] done clear
  C)
   \[\frac{RM}{RP}\]         done clear
  D)
   \[MR,MP\] done clear
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• question_answer14)
  Base of a right angled \[\Delta \,ABC\] is 16 times the base of another right angled triangle PQR and height of first right angled triangle is 1/6th of other?s height, then what will be ratio of area of first triangle to second triangle.
  A)
   \[16:3\]                         done clear
  B)
   \[8:3\]    done clear
  C)
   \[1:1\]                           done clear
  D)
   \[4:3\] done clear
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• question_answer15)
  Find the value of ?x? from the given figure below, if \[PS\parallel QR\]
  A)
   \[1.5\]or\[1\]                 done clear
  B)
   \[2\]  done clear
  C)
   \[\sqrt{2}\] or \[1.33\]                 done clear
  D)
   \[2\sqrt{2}\] or \[1.4\] done clear
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• question_answer16)
  In the adjacent figure, BA and BC are produced to meet CD and AD produced in E and F. Then \[\angle AED+\angle CFD\] is.
  A)
   \[70{}^\circ \]                          done clear
  B)
   \[35{}^\circ \]                                         done clear
  C)
   \[55{}^\circ \]    done clear
  D)
         \[75{}^\circ \]                              done clear
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• question_answer17)
  In an equilateral \[\Delta \,ABC,\text{ }AD\]is altitude, \[A{{D}^{2}}\] is equal to _______
  A)
   \[3C{{A}^{2}}\]                     done clear
  B)
   \[4B{{D}^{2}}\] done clear
  C)
   \[3C{{D}^{2}}\]         done clear
  D)
   \[C{{A}^{2}}\]                                                    done clear
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• question_answer18)
  In a right-angled \[\Delta \] as shown below. If \[{{z}^{2}}=2xy\]then find angle \[\theta \].
  A)
   \[55{}^\circ \]                          done clear
  B)
   \[65{}^\circ \] done clear
  C)
   \[40{}^\circ \]                          done clear
  D)
   \[45{}^\circ \] done clear
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• question_answer19)
  The triangle with measurements \[a=\left( \sqrt{m}-1 \right),\]\[b=2{{m}^{\frac{1}{4}}}\] and \[c=\left( \sqrt{m}+1 \right)\] is:
  A)
   Isosceles                       done clear
  B)
   Right angled triangle done clear
  C)
   Equilateral                             done clear
  D)
   Right angled isosceles done clear
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• question_answer20)
  Consider sides of some \[\Delta \]les. Determine which of them is / are right \[\Delta \](s)?

  (i) 10, 24, 26	(ii) 7, 8, 9
  (iii) 80, 90, 100	(iv) 2.5, 0.7, 2.4

  A)
   (i) & (ii)            done clear
  B)
   (ii) & (iii)       done clear
  C)
   (iii) & (iv)                      done clear
  D)
   (iv) & (i) done clear
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• question_answer21)
  Which of the blanks has been incorrectly filled against ticked answer?

  (i) All circles are ____________ (congruent similar ( Ö ).

  (ii) All squares are ___________(similar congruent (Ö )

  (iii) All ________ triangles are similar (isosceles equilateral (Ö ).

  (iv) Two polygons of the same number of sides are similar. If their corresponding angles are _______(equal proportional ( Ö ).

  A)
   (i)                                done clear
  B)
   (ii)                   done clear
  C)
   (iii)                               done clear
  D)
   (iv) done clear
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• question_answer22)
  In figure. Altitudes AD and CE of  \[\Delta \,ABC\]intersect each other at the point P. then
  A)
   \[\Delta \,AEP\sim \Delta \,CBP\] done clear
  B)
   \[\Delta \,ABD\sim \Delta \,CBE\] done clear
  C)
   \[\Delta \,AEP\cong \Delta \,ADB\]           done clear
  D)
   \[\Delta \,PDC\cong \Delta \,BEC\] done clear
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• question_answer23)
  Choose the correct answer: In\[\Delta \,LMN,\]\[LM=6\sqrt{3},\]\[LN=12\] and\[MN=6\]. Then \[ZM=\]_______
  A)
   \[100{}^\circ \]                        done clear
  B)
   \[60{}^\circ \]            done clear
  C)
   \[30{}^\circ \]                          done clear
  D)
   \[90{}^\circ \] done clear
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• question_answer24)
  In the given figure, \[\angle RPS=\angle RQP=90{}^\circ ,\]\[PQ=1,PS=2;QR=3;\] and right \[\angle s\]as shown. Measurement of \[PR+RS=\]________
  A)
   \[\sqrt{12}-\sqrt{10}\]                done clear
  B)
   \[\sqrt{17}+\sqrt{13}\] done clear
  C)
   \[\sqrt{2}\left( \sqrt{5}+\sqrt{7} \right)\] done clear
  D)
   \[\sqrt{10}+\sqrt[7]{2}\] done clear
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• question_answer25)
  In \[\Delta \]le PQR (See figure), \[\frac{PL}{LQ}=\frac{PM}{MR}\]. Nature of \[\Delta \,PQR\]is as follows:
  A)
   Acute angled triangle                             done clear
  B)
   Isosceles triangle         done clear
  C)
   Right triangle                             done clear
  D)
   Scalene triangle                                                  done clear
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• question_answer26)
  Semi-perimeters of two similar triangles PQR and LMN are 10 cm & 15 cm respectively. If LM = 9 cm, find PQ?                          
  A)
   18                                done clear
  B)
   6 cm   done clear
  C)
   8cm                             done clear
  D)
   13.5 cm                                       done clear
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• question_answer27)
  See the ladder placed on a 2 metre high concrete pedestal against the wall as below. Find height ?h? of the wall.
  A)
   32 m                            done clear
  B)
   18 m                                               done clear
  C)
   30 m                            done clear
  D)
   17 m    done clear
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• question_answer28)
                                          Two 26 m strings are tied to a concrete pedestal between two poles having heights of 24 m and 25 m respectively. What is the distance between the poles? (Consider the top of pedestal to be on the same level as the base of the poles).
  A)
   15 m                            done clear
  B)
   21 m          done clear
  C)
   17 m      done clear
  D)
   28 m done clear
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• question_answer29)
  A student of height 1m is walking away from the base of a street light at a speed of 0.5 m/sec. If the street light is 5m above the ground, find the length of the student's shadow after 8 seconds.
  A)
   \[2\text{ }m\]                            done clear
  B)
   \[1\text{ }m\]      done clear
  C)
   \[\sqrt{3}\text{ }m\]                  done clear
  D)
   \[\sqrt{2}\text{ }m\] done clear
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• question_answer30)
  In the given figure, \[PQ\bot QR,\text{ }KL\bot PR\] and \[MN\bot QR\]. Which of the following is correct?               
  A)
   \[\Delta \,PLK\sim \Delta \,MRN\] done clear
  B)
   \[\angle y=\angle w\] done clear
  C)
   \[\Delta \,PKL\sim \Delta MRN\] done clear
  D)
   \[\angle x=\angle z\] done clear
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