Question

The areas of two similar triangles ABC and PQR are $25c{m}^2\&49c{m}^2$, respectively. If QR $=9.8$ cm, then BC is:

• A. 9.8 cm
• B. 7 cm
• C. 49 cm
• D. 25 cm

Answer 1

The correct option is B 7 cm

Given: $\frac{ar\left(ABC\right)}{ar\left(PQR\right)}=\frac{25}{49}$

In two similar triangles, the ratio of their areas will be equal to the square of the ratio of their sides.

Hence in $△ABC$ and $△PQR,$

$\Rightarrow {\left(\frac{BC}{QR}\right)}^2=\frac{ar△ABC}{ar△PQR}$

$\Rightarrow {\left(\frac{BC}{QR}\right)}^2=\frac{25}{49}$

$\Rightarrow \frac{BC}{QR}=\frac{5}{7}$

$\Rightarrow \frac{BC}{9.8}=\frac{5}{7}$

$\Rightarrow BC=\frac{5}{7}\times 9.8=7$