Question

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

Answer 1

Let ∆ABC and ΔPQR are similar triangles. The area of triangles is 169cm² and 121cm², respectively.

Longest side of the larger triangle is 26cm

TO FIND: length of longest side of the smaller side.

Suppose longest side of the larger triangle is BC and longest side of the smaller triangle is QR.

We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

Hence,

`(ar(Δ ABC))/(ar(Δ PQR))=(BC^2)/(QR^2)`

`169/121=26^2/(QR^2)`

`13/11=26/(QR)`

`QR=(11xx26)/13`

`QR=22`

`QR= 22cm`