Question

The area of two similar triangles are 36 cm² and 100 cm². If the length of a side of the smaller triangle in 3 cm, find the length of the corresponding side 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 triangle)}/\text{(Area of larger  triangle)}=\text{(Corresponding side of smaller triangle)}^2/\text{(Corresponding side of larger triangle)}^2`

`36/100=3^2/\text{(Corresponding side of larger triangle)}^2`

`\text{(Corresponding side of larger triangle)}^2= (9xx100)/(36)`

`\text{(Corresponding side of larger triangle)}^2 100/4`

`\text{(Corresponding side of larger triangle)}^2=25`

`\text{(Corresponding side of larger triangle)}^2= 5`

Hence, the length of the corresponding side of the larger triangle is  `5 cm`