Question

The perimeter of two similar triangles are 81 cm and 63 cm respectively. If one side of the first triangle be 18 cm, then the corresponding side of the smaller triangle is ___ cm long.

• A. 14
• B. 16
• C. 18
• D. 20

Answer 1

The correct option is A

14

Let the perimter of the similar triangles be $P_1$ and $P_2$ respectively.

Since two triangles ABC and DEF are similar, their perimeters will be proportional to the corresponding sides of the two triangles.

$\Rightarrow \frac{Perimete{r}_1}{perimete{r}_2}=\frac{18}{x}$

where x is side length of corresponding side of smaller triangle.

$\Rightarrow \frac{81}{63}=\frac{18}{x}$
$\Rightarrow$ x = 14 cm

Hence, the corresponding side of the smaller triangle is 14 cm long.