Question

In $△ABC\sim △DEF$, BC $=$ 4 cm, EF $=$ 5 cm and area($△$ABC)$=$ 80 $c{m}^2$, the area($△$ DEF) is:

• A. $100c{m}^2$
• B. $125c{m}^2$
• C. $150c{m}^2$
• D. $200c{m}^2$

Answer 1

Answer: (B)

$125c{m}^2$

Given $△ABC\sim △DEF$

In two similar triangles, the ratio of their areas is the square of the ratio of their sides

$\Rightarrow \frac{ar\left(ABC\right)}{ar\left(DEF\right)}={\left(\frac{BC}{EF}\right)}^2\Rightarrow \frac{80}{ar\left(DEF\right)}={\left(\frac{4}{5}\right)}^2\Rightarrow \frac{80}{ar\left(DEF\right)}=\frac{16}{25}\Rightarrow ar\left(DEF\right)=125{cm}^2$