Question

$△RST\sim △XYZ.$ In $△RST$, $RS=4.5$ cm, $\angle RST={40}^{\circ }$, $ST=5.7$ cm Construct $△RST$ and $△XYZ$, such that $\frac{RS}{XY}=\frac{3}{5}$.

Answer 1

Construct $△RST$ such that $RS=4.5$ cm, $\angle RST={40}^{\circ }$ and $ST=5.7$ cm.
$△RST$ and $△XYZ$ are similar.
So, their corresponding sides are proportional and corresponding angles are equal.
$\therefore \frac{RS}{XY}=\frac{ST}{YZ}=\frac{RT}{XZ}=\frac{3}{5}$
$\Rightarrow \frac{4.5}{XY}=\frac{5.7}{YZ}=\frac{3}{5}$
$\Rightarrow XY=\frac{5}{3}\times 4.5=7.5cm,YZ=\frac{5}{3}\times 5.7=9.5$ cm
Also, $\angle XYZ=\angle RST={40}^{\circ }$
Now, construct $△XYZ$ such that $XY=7.5$ cm, $\angle XYZ={40}^{\circ }$ and $YZ=9.5$ cm.