Question

Sides of two similar triangles are in the ratio $4:9$.Area of these triangles are in the ratio

• A. $2:3$
• B. $4:9$
• C. $81:16$
• D. $16:81$

Answer 1

Answer: (D)

$16:81$

Given:Ratio of sides of similar triangles$=\frac{4}{9}$

We know that if two triangles are similar,

ratio of areas is equal to the ratio of squares of corresponding sides.

So, $\frac{areaoftriangle1}{areaoftriangle2}=\frac{{\left(sideoftriangle1\right)}^2}{{\left(sideoftriangle2\right)}^2}$

$\frac{areaoftriangle1}{areaoftriangle2}={\left(\frac{4}{9}\right)}^2=\frac{16}{81}$

$\frac{areaoftriangle1}{areaoftriangle2}=\frac{16}{81}$