Question

The corresponding sides of two similar triangles are in the ratio $1:3$ . If the area of the smaller triangle is 40 $c{m}^2$, find the area of the larger triangle.

Answer 1

Hint – Whenever you come across this type of problem, always use the concept that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Complete step by step answer:
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
$\therefore$ $\left[{\displaystyle \frac{{\left(\text{Side of the smaller triangle}\right)}^{\text{2}}}{{\left(\text{Side of the larger triangle}\right)}^{\text{2}}}}\right]\text{ = }\left({\displaystyle \frac{\text{Area of the smaller triangle}}{\text{Area of the larger triangle}}}\right)$
Let the area of the larger triangle be x
Now we know that the ratio of sides of the triangles = ${\displaystyle \frac{1}{3}}$
Hence ${\left({\displaystyle \frac{1}{3}}\right)}^2={\displaystyle \frac{40}{x}}$
$\Rightarrow {\displaystyle \frac{1}{9}}={\displaystyle \frac{40}{x}}$
$\Rightarrow x=40\times 9$
$\Rightarrow x=360\text{ c}{\text{m}}^2$

Area of the larger triangle is 360 $c{m}^2$.

Note - Whenever you come to this type of problem first let assume a variable for unknown and after that apply the theorem of triangles (The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides) And easily get the required answer.