Question Bank for 10th Class Mathematics Triangles Case Based (MCQs) - Triangles

To find the distance between the points, he makes a right-angled triangle using rope connecting Q with another point R at a distance of \[\text{4m},\] connecting R to point 5 at a distance of \[\text{15m}\] from point R and connecting S to the point P which is at a distance of \[\text{8m}\] from S such that triangle PRS is a right angled triangle with \[\angle S=90{}^\circ \].

Based on the above information, give the answer of the following questions:

Which property of geometry will be used to find the distance PR?

A)

Similarity of triangles

B)

Thales theorem

C)

Pythagoras theorem

D)

Area of similar triangles

View Solution

2)

What is the distance (PQ) of garden?

A)

\[10\,m\]

B)

\[11\,m\]

C)

\[12\,m\]

D)

\[13\,m\]

View Solution

3)

What is the distance PR?

A)

\[12\,m\]

B)

\[17\,m\]

C)

\[10\,m\]

D)

\[9\,m\]

View Solution

4)

Find the Length of the rope used.

A)

\[26\,m\]

B)

\[25\,m\]

C)

\[27\,m\]

D)

\[23\,m\]

View Solution

5)

Which of the following forms a Pythagoras triplet?

A)

\[(5,11,13)\]

B)

\[(9,15,18)\]

C)

\[(17,24,25)\]

D)

\[(20,21,29)\]

View Solution

6)

Direction: Q. 6 to 10

Anika is studying in class X. She observe two poles DC and BA. The heights of these poles are x m and y m respectively as shown in figure below:

These poles are z metres apart and O is the point o:

intersection of the lines joining the top of each pole to the foot of opposite pole and the distance between point 0 and L is a Few questions came" to his mind while observing the poles Give answer to his questions by looking at figure.

Which is the correct similarity criteria applicable in \[\Delta CAB\] and \[\Delta CLO\]?

A)

AA

B)

SSS

C)

SAS

D)

RHS

View Solution

7)

If \[\text{CL}=\text{a},\]then find o In terms of x, y and d.

A)

\[\frac{xd}{z}\]

B)

\[\frac{xz}{d}\]

C)

\[\frac{zd}{x}\]

D)

\[xzd\]

View Solution

8)

If \[\text{AL}=\text{b},\]then find b in terms of x, y and d is:

A)

\[\frac{zd}{y}\]

B)

\[\frac{yd}{z}\]

C)

\[xyd\]

D)

\[xzd\]

View Solution

9)

Find d in terms of x and y.

A)

\[\frac{x+y}{xy}\]

B)

\[\frac{xy}{x+y}\]

C)

\[xy\]

D)

\[\frac{x}{y}\]

View Solution

10)

If \[\text{x}=\text{7 m}\] and \[\text{y}=\text{1}0\text{ m},\]then find d.

A)

\[\frac{30}{13}m\]

B)

\[\frac{50}{17}m\]

C)

\[\frac{70}{17}m\]

D)

\[\frac{90}{19}m\]

View Solution

11)

Direction: Q. 11 to 15

Gaurav placed a light bulb at a point O on the ceiling and directly below it placed a table. He cuts a polygon, say a quadrilateral PQRS, from a plane cardboard and place this cardboard parallel to the ground between the lighted bulb and the table. Then a shadow of PQRS is cast on the table as PQRS. Quadrilateral P'Q'R'S' is an enlargement of the quadrilateral PQRS with scale factor \[\text{1}:\text{3}\] Given that \[\text{PQ}=\text{2}.\text{5cm},\] \[\text{QR}=\text{3}.\text{5 cm}\]. \[\text{RS}=\text{3}.\text{4 cm}\] and \[\text{PS}=\text{3}.\text{1 cm};\] \[\angle P=115{}^\circ ,\] \[\angle Q=95{}^\circ ,\] \[\angle R=65{}^\circ \]and \[\angle S=85{}^\circ \].

Based on the given information, give the answer of the following questions:

The length of R'S' is:

A)

\[\text{3}.\text{4 cm}\]

B)

\[\text{1}0.\text{2 cm}\]

C)

\[\text{6}.\text{8 cm}\]

D)

\[\text{9}.\text{5 cm}\]

View Solution

12)

The ratio of sides P'Q' and Q'R' is:

A)

\[\text{5}:7\]

B)

\[7:5\]

C)

\[7:2\]

D)

\[2:7\]

View Solution

13)

The measurement of angle Q is:

A)

\[115{}^\circ \]

B)

\[95{}^\circ \]

C)

\[65{}^\circ \]

D)

\[85{}^\circ \]

View Solution

14)

The sum of the length Q'R' and P'S' is:

A)

\[\text{12}.\text{3 cm}\]

B)

\[\text{6}.\text{7 cm}\]

C)

\[\text{19}.\text{8 cm}\]

D)

\[\text{9 cm}\]

View Solution

15)

The sum of angles of quadrilateral P'Q'R'S' is:

A)

\[180{}^\circ \]

B)

\[270{}^\circ \]

C)

\[300{}^\circ \]

D)

\[360{}^\circ \]

View Solution

16)

Direction: Q. 16 to 20

There is a staircase as shown in figure, connecting points A and B. Measurement of steps are marked in the figure. Give answers of the following questions by looking at the figure.

The common angle in each staircase is:

A)

\[30{}^\circ \]

B)

\[60{}^\circ \]

C)

\[90{}^\circ \]

D)

nothing

View Solution

17)

Which is the correct similarity criteria applicable for staircase II and III?

A)

RHS

B)

SAS

C)

SSA

D)

AAS

View Solution

18)

Which concept is used to find the distance between A and S?

A)

Pythagoras theorem

B)

Thales theorem

C)

Converse of Thales theorem

D)

Converse of pythagoras theorem,

View Solution

19)

The straight line distance between A and B is:

A)

\[\sqrt{5}+\sqrt{6.56}+\sqrt{6.56}+\sqrt{7.24}\]

B)

\[\sqrt{5.15}+\sqrt{6.21}+\sqrt{6.21}+\sqrt{7}\]

C)

\[\sqrt{5}+\sqrt{6}+\sqrt{6}+\sqrt{7}\]

D)

None of the above

View Solution

20)

The sum of the area of each staircase is:

A)

6 square unit

B)

12 square unit

C)

10 square unit

D)

None of these

View Solution

21)

Direction: Q. 21 to 25

Nazima is fly fishing in a stream. The tip of her fishing rod is \[\text{1}.\text{8 m}\] above the surface of the water and the fly at the end of the string rests on the water \[3.6\text{ m}\]away and \[2.4\text{ m}\] from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, answer the following questions given below:

How much string does she have out?

A)

\[1\,m\]

B)

\[1.5\,m\]

C)

\[2.5\,m\]

D)

\[3\,m\]

View Solution

22)

If she pulls in the string at the rate of \[\text{5 cm}/\text{s}\] then the Length of the string pulled in 12 seconds is:

A)

\[0.\text{6 m}\]

B)

\[1.\text{6 m}\]

C)

\[0.8\text{ m}\]

D)

\[1.2\text{ m}\]

View Solution

23)

Length of the remaining string left out after 12 seconds is:

A)

\[1.2\text{ m}\]

B)

x

C)

D)

View Solution

24)

The distance of fly at the end of the string from the point over the water surface just below the tip of fishing rod, after 12 seconds is:

A)

\[\text{1}.\text{2 m}\]

B)

\[\text{2}.\text{52 m}\]

C)

\[\text{1}.\text{59 m}\]

D)

\[\text{2}.\text{79 m}\]

View Solution

25)

The horizontal distance of the fly from Nazima after 12 seconds is:

A)

\[1.2\,m\]

B)

\[\text{2}.\text{52 m}\]

C)

\[\text{1}.\text{59 m}\]

D)

\[\text{2}.\text{79 m}\]

View Solution

26)

Direction: Q. 26 to 30

Two buildings I and II are of heights \[\text{19 m}\] and \[\text{4}0\text{ m}\] respectively \[20\text{ m}\] apart.

Based on the above information, give the answer of the following questions:

The distance between their tops can be found out by using which of the following theorems?

A)

Similarity of triangles

B)

Converse of Pythagoras Theorem

C)

Thales Theorem

D)

Pythagoras Theorem

View Solution

27)

The distance between their tops i.e., Length of AB is:

A)

\[\sqrt{1961}\,m\]

B)

\[\sqrt{802}\,m\]

C)

\[29\,m\]

D)

\[41\,m\]

View Solution

28)

In a \[\Delta ABC,\] \[BD\bot AC\] such that \[B{{D}^{2}}=DC.\] AD, then :

A)

\[\angle A=90{}^\circ \]

B)

\[\angle B=90{}^\circ \]

C)

\[\angle C=90{}^\circ \]

D)

ABC is not a right angled triangle

View Solution

29)

In the given figure, the side PQ of a right triangle \[\Delta PQR\]where \[\text{OP}=\text{6 cm},\] \[\text{OR}=\text{8 cm}\] and \[\text{QR}=\text{26 cm},\]is :

A)

\[21\,cm\]

B)

\[23\,cm\]

C)

\[24\,cm\]

D)

\[36\,cm\]

View Solution

30)

Hypotenuse of a right triangle is \[\text{25 cm}\] and out of the remaining two sides, one is longer than the other by \[\text{5 cm}\]. Then the length of the longer side is:

A)

\[20\,cm\]

B)

\[15\,cm\]

C)

\[12.5\,cm\]

D)

\[10\,cm\]

View Solution

31)

Direction: Q. 31 to 35

The Louvre Pyramid (Pyramide du Louvre) is a large glass and Chinese- American architect I.

M. Pei, surrounded by three smaller pyramids, in the maincourtyard (Cour Napoleon) of the Louvre Palace (Palais du Louvre) in Paris. The large pyramid serves as the main entrance to the Louvre Museum.

Completed in 1989., it has become a landmark of the city of Paris. As can be seen, two triangles ABC and DEF have been marked in the image, where \[\left. DE \right\|AB\] and \[\left. EF \right\|BC\].

Based on the given information, give the answer of the following questions:

Which of the following is not a criteria for similarity of two triangles?

A)

SSS

B)

ASA

C)

SAS

D)

AA

View Solution

32)

Select the correct statement from the statements given below:

A)

\[\Delta ABC\tilde{\ }\Delta DEF\] by SSS similarity criterion

B)

\[\Delta ABC\tilde{\ }\Delta DEF\] by SAS similarity criterion

C)

\[\Delta ABC\tilde{\ }\Delta EDF\] by AA similarity criterion

D)

\[\Delta ABC\tilde{\ }\Delta DEF\] by AA similarity criterion

View Solution

33)

If the measures of sides AB, BC and DE are \[\text{15 m},\] \[\text{21 m},\] and \[\text{10 m}\] respectively, then measure of side EF is:

A)

\[\text{14 m}\]

B)

\[\frac{50}{7}\text{ m}\]

C)

\[\text{12 m}\]

D)

\[\text{7 m}\]

View Solution

34)

In relation to the part \[(3),\] the ratio of sides \[\text{DF}:\text{AC}\] is:

A)

\[2:5\]

B)

\[5:2\]

C)

\[2:3\]

D)

\[3:2\]

View Solution

35)

In relation to the part \[(3),\] the ratio of areas of triangles ABC and DEF is:

A)

\[9:4\]

B)

\[3:2\]

C)

\[4:9\]

D)

\[2:3\]

View Solution

10th Class Mathematics Triangles Question Bank

done Case Based (MCQs) - Triangles Total Questions - 35

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Case Based (MCQs) - Triangles

Case Based (MCQs) - Triangles Total Questions - 35