10th Class Mathematics Solved Paper - Mathematics-2018

  • question_answer 26) Draw a triangle ABC with \[BC=6\text{ }cm,\text{ }AB=5\text{ }cm\] and \[\angle ABC=60{}^\circ \]. Then construct a triangle whose sides are \[\frac{3}{4}\] of the corresponding sides of the \[\Delta \,ABC\].

    Answer:

    Steps of construction -
    (i) Draw a line segment \[BC=6\text{ }cm\].
    (ii) Construct \[\angle XBC=60{}^\circ \].
    (iii) With B as centre and radius equal to 5 cm, draw an arc intersecting XB at A.
    (iv) Join AC. Thus, \[\Delta \text{ }ABC\]is obtained.
    (v) Draw an acute angle \[\angle CBY\] below of B.
    (vi) Mark 4-equal parts on BY as \[{{B}_{1}},{{B}_{2}},{{B}_{3}}\] and \[{{B}_{4}}\].
    (vii) Join \[{{B}_{4}}\]to C.
    (viii) From \[{{B}_{3}}\] draw a line parallel to \[{{B}_{4}}C\]intersecting BC at C.
    (ix) Draw another line parallel to CA from C?, intersecting AB at A?.
    (x) \[\Delta \,A'BC'\] is required triangle which is similar to \[\Delta \,ABC\] such that \[BC'=\frac{3}{4}BC\].


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