Question

$△$ABC and $△$PQR are similar triangles. If $\frac{AB}{PQ}=\frac{4}{5}$ , find the ratio of areas of $△$ABC and $△$PQR.

• A. 4 : 5
• B. 5 : 4
• C. 16 : 25
• D. 25 : 16

Answer 1

The correct option is C 16 : 25

$△$ABC and $△$PQR are similar triangles.

We know that $\frac{\left(Areaof△ABC\right)}{\left(Areaof△PQR\right)}=\frac{A{B}^2}{P{Q}^2}$

$\frac{\left(Areaof△ABC\right)}{\left(Areaof△PQR\right)}=\frac{4^2}{5^2}=\frac{16}{25}$

Area of $△$ABC : Area of $△$ PQR = 16 : 25