Question

In given figure $△ABC$ and $△DEF$ are similar, $BC=3cm$, $EF=4cm$, and area of triangle $ABC=54c{m}^2$ find the area of $△DEF$ in __ $c{m}^2$

Answer 1

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

$\therefore \frac{\text{Area of triangle ABC}}{\text{Area of triangle DEF}}=(\frac{BC}{DF}{)}^2$

$\Rightarrow \frac{54}{\text{Area of triangle DEF}}=(\frac{3}{4}{)}^2$

$\Rightarrow \frac{54}{\text{Area of triangle DEF}}=\frac{9}{16}$

$\Rightarrow$ Area of triangle $DEF=\frac{16}{9}\times 54$

$\therefore$ Area of triangle $DEF=16\times 6=96c{m}^2$