Question

The areas of two similar triangles are 169cm² and 121cm² respectively. If one side of the larger triangle is 26cm, find the length of the corresponding side of the smaller triangle.

Answer 1

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

∴ `("area"(Δ"ABC"))/("area"(Δ"PQR")) = "AB"^2/"DE"^2` 

⇒ `(169)/(121) = (26^2)/"DE"^2`

⇒ DE² = `(121 xx 676)/(169)`

⇒ DE² = 484
⇒ DE = 22cm.