Question

The areas of two similar triangles ∆ABC and ∆PQR are 25 cm² and 49 cm² respectively. If QR = 9.8 cm, find BC.

Answer 1

It is being given that ∆ABC ~ ∆PQR, ar (∆ABC) = 25 cm² and ar (∆PQR) = 49 cm².

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

`\therefore \text{ }\frac{ar\ (\Delta ABC)}{ar\ (\DeltaPQR)}=\frac{BC^{2}}{QR^{2}}`

`\Rightarrow \frac{25}{49} = \frac{x^{2}}{(9.8)^{2}}`

`\Rightarrowx^{2} = (\frac{25}{49}\times 9.8\times 9.8)`

`\Rightarrow x = \sqrt{\frac{25}{49}\times 9.8\times 9.8}`

`\Rightarrow x = (5/7xx9.8)`

`\Rightarrow x = (5xx1.4)`

`\Rightarrow x = 7`

Hence, BC = 7 cm.