Question

$\Delta ABC\sim \Delta DEF$, with AB = 5 cm and DE = 8 cm.
If the area of $\Delta ABC$ is $50c{m}^2$, what will be the area of $\Delta DEF$ ?

• A. $124c{m}^2$
• B. $128c{m}^2$
• C. $120c{m}^2$
• D. $118c{m}^2$

Answer 1

The correct option is B

$128c{m}^2$

Given: $\Delta ABC\sim \Delta DEF$
Area of $\Delta ABC=50c{m}^2$
AB = 5 cm and DE = 8 cm

Now, we know that if, $\Delta ABC\sim \Delta DEF$,

then, $\frac{\text{Ar}\left(\Delta ABC\right)}{\text{Ar}\left(\Delta DEF\right)}=\frac{A{B}^2}{D{E}^2}=\frac{A{C}^2}{D{F}^2}=\frac{B{C}^2}{E{F}^2}$

So, $\frac{\text{Ar}\left(\Delta ABC\right)}{\text{Ar}\left(\Delta DEF\right)}=\frac{A{B}^2}{D{E}^2}=\frac{(5cm{)}^2}{(8cm{)}^2}=\frac{25c{m}^2}{64c{m}^2}$

$\Rightarrow \frac{50c{m}^2}{\text{Ar}\left(\Delta DEF\right)}=\frac{25}{64}$

$\Rightarrow Ar\left(\Delta DEF\right)=\frac{50\times 64}{25}c{m}^2=128c{m}^2$.