Question

$△ABC$ and $△PQR$ are similar triangle such that area $\left(△ABC\right)=49{cm}^2$ and Area $\left(△PQR\right)=25{cm}^2$. If $AB=5.6cm$, find the length of $PQ$.

• A. $4cm$
• B. $5cm$
• C. $5.6cm$
• D. $7cm$

Answer 1

The correct option is A $4cm$

Ar. ($△ABC$) = $49c{m}^2$
Ar. ($△PQR$) = $25c{m}^2$
$AB=5.6cm$
For similar triangles the ratio of areas is equal to the ratio of square of its sides.
Thus, $\frac{A\left(△ABC\right)}{A\left(△PQR\right)}=\frac{A{B}^2}{P{Q}^2}$
$\frac{49}{25}=\frac{(5.6{)}^2}{P{Q}^2}$
$P{Q}^2=\frac{31.36\times 25}{49}$
$P{Q}^2=16$
$PQ=4$cm