Question

Construct a triangle similar to a given triangle $ABC$ with its side equal to $\frac{5}{3}$ of corresponding side of triangle $ABC$ (i.e., of scale factor $\frac{5}{3}$).

Answer 1

Refer fig, 1

Here, we are given $\Delta ABC$ and scale factor $3$

$\therefore$ scale factor $<1$

We need to construct $\Delta$ similar to $\Delta ABC$

Let's follow these steps

(1) Draw any rays $BX$ making an acute angle with $BC$ on the side opposite to the vertex $A$

(2) Hark $4$ (the greater $y_3$ and $4$ in $\frac{3}{4}$)

points $B_1,B_2,B_3$ $B_4$ on $BX$ so that $B{B}_1=B_2{B}_3=B_2{B}_1=B_3{B}_4$

(3) Join $B_{4}C$ and draw the line through $B_3||$ to $B_{4}C$

Refer fig. 2

(4) draw a line $C^{\prime }||$ to $CA$ to intersect $BA$ to $A$

Thus $\Delta AB{C}^{\prime }$ is the required $\Delta$