Question

If $△ABC\sim △DEF$, $BC=4cm$ and $EF=5cm$ and ar $\left(△ABC\right)=80c{m}^2$,the ar$\left(△DEF\right)$ is

• A. $120c{m}^2$
• B. $125c{m}^2$
• C. $150c{m}^2$
• D. $200c{m}^2$

Answer 1

The correct option is B $125c{m}^2$

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

$\therefore \frac{ar\left(△ABC\right)}{ar\left(△DEF\right)}=\frac{B{C}^2}{E{F}^2}$

$\Rightarrow \frac{80}{ar\left(△DEF\right)}=\frac{4^2}{5^2}$

$\Rightarrow \frac{80}{ar\left(△DEF\right)}=\frac{16}{25}$

$\Rightarrow ar\left(△DEF\right)=\frac{80\times 25}{16}=125$

Hence, the area of $\Delta DEF$ is $125c{m}^2$