Question

$△ABC\sim △DEF$. IF $BC=4cm$, $EF=5cm$ and area $\left(△ABC\right)=32{cm}^2$, determine the area of $△DEF$.

• A. $50m^2$
• B. $40m^2$
• C. $40{cm}^2$
• D. None of these
  

Answer 1

The correct option is D None of these

Ar. ($△ABC$) = $32c{m}^2$
$BC=4cm$
$EF=5cm$
For similar triangles the ratio of areas is equal to the ratio of square of its sides.
Thus, $\frac{A\left(△ABC\right)}{A\left(△DEF\right)}=\frac{B{C}^2}{E{F}^2}$
$\frac{32}{A\left(△DEF\right)}=\frac{4^2}{5^2}$
$A\left(△DEF\right)=\frac{32\times 25}{16}$
$A\left(△DEF\right)=50c{m}^2$