Question

∆RST ~ ∆XYZ. In ∆RST, RS = 4.5 cm, ∠RST = 40°, 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, ∠RST = 40° and ST = 5.7 cm.
∆RST and ∆XYZ are similar.
So, their corresponding sides are proportional and corresponding angles are equal.

\[\therefore \frac{RS}{XY} = \frac{ST}{YZ} = \frac{RT}{XZ} = \frac{3}{5}\]

\[\Rightarrow \frac{4 . 5}{XY} = \frac{5 . 7}{YZ} = \frac{3}{5}\]

\[\Rightarrow XY = \frac{5}{3} \times 4 . 5 = 7 . 5 \text{ cm }, YZ = \frac{5}{3} \times 5 . 7 = 9 . 5 \] cm

Also, ∠XYZ = ∠RST = 40°

Now, construct ∆XYZ such that XY = 7.5 cm, ∠XYZ = 40° and YZ = 9.5 cm.