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 \[\Delta \text{ }ABC\].
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