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.

${\displaystyle \therefore \frac{ar (\Delta ABC)}{ar (\Delta PQR)}=\frac{B{C}^2}{Q{R}^2}}$

${\displaystyle \Rightarrow \frac{25}{49}=\frac{x^2}{{\left(9.8\right)}^2}}$

${\displaystyle \Rightarrow x^2=(\frac{25}{49}\times 9.8\times 9.8)}$

${\displaystyle \Rightarrow x=\sqrt{\frac{25}{49}\times 9.8\times 9.8}=(\frac{5}{7}\times 9.8)=(5\times 1.4)=7}$

Hence BC = 7 cm.