question_answer

Construct a triangle ABC in which \[BC=6\text{ }cm,\text{ }AB=5\text{ }cm\] and \[\angle ABC=60{}^\circ \].

Then construct another triangle whose sides are \[\frac{3}{4}\] times the corresponding sides of \[\Delta \text{ }ABC\]

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 which intersect XB at A.

(iv) Join AC. Thus, \[\Delta \text{ }ABC\] is obtained.

(v) Draw D on BC such that \[BD=\frac{3}{4}BC=\left( \frac{3}{4}\times 6 \right)cm=\frac{9}{2}cm=4.5\,cm\]

(vi) Draw \[DE\parallel CA\], cutting BA at E.

Then, \[\Delta \text{ }BDE\]is the required triangle similar to \[\Delta \text{ }ABC\]such that each side of \[\Delta \text{ }BDE\] is \[\frac{3}{4}\] times the corresponding side of\[\Delta \text{ }ABC\].