Question

The areas of two similar triangle are 36 ${cm}^2$ and 100 ${cm}^2$. If the length of a side of the smaller triangle in 3 cm, find the corresponding side of the larger triangle.

Answer 1

Given, area of smaller triangle $=36c{m}^2$ and area of larger triangle $=100c{m}^2$

Also, length of a side of the smaller triangle $=20cm$

Let length of the corresponding side of the larger triangle $=xcm$

By property of area of similar triangle,

$\frac{ar\left(largertriangle\right)}{ar\left(smallertriangle\right)}=\frac{(sideoflargertriangle{)}^2}{(sideofsmallertriangle{)}^2}$

$\therefore$ $\frac{100}{36}=\frac{x^2}{3^2}$

$\therefore$ $x^2=\frac{100\times 9}{36}$

$\therefore$ $x^2=25$

$\therefore$ $x=5cm$

$\therefore$ Length of the corresponding side of the larger triangle Is $5cm$