Question

The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 12 cm, determine the corresponding side of the second triangle.

Answer 1

Let $△ABC$ and $△DEF$ be two similar triangles of perimeters $P_1$ and $P_2$ respectively.

Also, let AB=12 cm, $P_1$=30 cm and $P_2$=20 cm.

Then,

$\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{P_1}{P_2}$ [$\because$ Ration of corresponding sides of similar triangles is equal to the ratio of their perimeters]

$\Rightarrow$ $\frac{AB}{DE}=\frac{P_1}{P_2}$

$\Rightarrow$ $\frac{12}{DE}=\frac{30}{20}$

$\Rightarrow$ $DE=\frac{12\times 20}{30}cm=8cm$

Hence, the corresponding side of the second triangle is 8 cm