Question

The areas of two similar triangles ΔABC and ΔPQR are 25 cm² and 49 cm², respectively, and QR = 9.8 cm. Find BC.
(a) 5 cm
(b) 8 cm
(c) 7 cm
(d) 6.3 cm

Answer 1

(c) 7 cm
It is given that $△ABC~△PQR$.
$ar\left(△ABC\right)=25{\mathrm{cm}}^2\mathrm{and}\mathrm{a}\mathrm{r}\left(△\mathrm{PQR}\right)=49{\mathrm{cm}}^2$
Also, QR = 9.8 cm. We have to find BC.
We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
∴ $\frac{ar\left(△ABC\right)}{ar\left(△PQR\right)}=\frac{B{C}^2}{Q{R}^2}$
$\Rightarrow {\left({\displaystyle \frac{BC}{QR}}\right)}^2=\frac{ar\left(△ABC\right)}{ar\left(△PQR\right)}=\frac{25}{49}={\left(\frac{5}{7}\right)}^2$

$$\begin{gathered} \Rightarrow \frac{BC}{QR}=\frac{5}{7} \\ \Rightarrow \frac{BC}{9.8}=\frac{5}{7} \end{gathered}$$
$\Rightarrow BC=\frac{\left(5\times 9.8\right)}{7}=\frac{49}{7}=7$
Hence, BC = 7 cm.