Question

If $△ABC$ is similar to $△DEF$ such that BC=3 cm, EF=4 cm and area of $△ABC=54{cm}^2$. Determine the area of $△DEF$.

• A. $40c{m}^2$
• B. $59c{m}^2$
• C. $69c{m}^2$
• D. $96c{m}^2$

Answer 1

The correct option is D $96c{m}^2$

Since the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

$\therefore$ $\frac{Area\left(△ABC\right)}{Area\left(△DEF\right)}=\frac{{BC}^2}{{EF}^2}$

$\Rightarrow$ $\frac{54}{Area\left(△DEF\right)}=\frac{3^2}{4^2}$

$\Rightarrow$ $Area\left(△DEF\right)=\frac{54\times 16}{9}=96{cm}^2$