Question

Corresponding sides of two triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm², determine the area of the larger triangle.

Answer 1

The ratio of the areas of two similar triangles is equal to the ratio of the square of any two corresponding sides.

`\text{(Area of triangle)}/\text{(Area of larger  triangle)}=\text{(Corresponding side of smaller triangle)}^2/\text{(Corresponding side of larger triangle)}^2`

`\text{(Area of triangle)}/\text{(Area of larger  triangle)}= 2^2/3^2`

`48/\text{(Area of larger  triangle)}= 4/9`

Area of larger  triangle =`(48xx9)/4`

Area of larger  triangle = 108

Hence the area of the larger triangle is  ` 108 cm^2`