Question

Question 12
Areas of two similar triangles are $36m^2$ and $100c{m}^2$. If the length of a side of the larger triangle is 20 cm. Find the length of the corresponding side of the smaller triangle.

Answer 1

Given, area of smaller triangle = $36m^2$ and area of larger triangle = $100c{m}^2$
Also, length of a side of the larger triangle = 20 cm

Let the length of the corresponding side of the smaller triangle = x cm

By property of area of similar triangle,

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

$\Rightarrow \frac{100}{36}=\frac{(20{)}^2}{x^2}\Rightarrow x^2=\frac{(20{)}^2\times 36}{100}$

$\Rightarrow x^2=\frac{400\times 36}{100}=144\therefore x=\sqrt{144}=12cm$

Hence, the length of corresponding side of the smaller triangle is 12 cm.