question_answer

Construct a triangle ABC with \[BC=7\text{ }cm,\text{ }\angle B=60{}^\circ \] and \[AB=6\text{ }cm\]. Construct another triangle whose sides are \[\frac{3}{4}\] times the corresponding side of \[\Delta \,ABC\].

Answer:

Steps of Construction-

(i) Draw a line segment \[AB=6\text{ }cm\].

(ii) Construct \[\angle ABX=60{}^\circ \].

(iii) From B as centre draw an arc of 7 cm cutting BX at C.

(iv) Join AC.

Thus \[\Delta \text{ }ABC\] is obtained.

(v) Take point D on AB such that \[AD=\frac{3}{4}AB=\left( \frac{3}{4}\times 6 \right)cm=\frac{9}{2}cm=4.5cm\]

(vi) Draw \[DE\parallel BC\], meeting AC at E. Then, \[\Delta \,ADE\]is the required triangle similar to \[\Delta \text{ }ABC\] such that each side of \[\Delta \,ADE\] is \[\frac{3}{4}\] times the corresponding side of \[\Delta \text{ }ABC\].