Question

Corresponding sides of two similar triangles are in the ratio 1 : 3. If the area of the smaller triangle in 40 cm², find the area of the larger triangle.

Answer 1

Since the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

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

`\text{(Area of smaller triangle)}/\text{(Area of larger  triangle)}1^2/3^2`

`40/\text{(Area of larger  triangle)}1/9`

Area of larger  triangle `= (40xx9)/(1) = 360 cm^2`

Hence the area of the larger triangle is  360` cm^2`