Question

In similar triangles $△ABC$ and $△FDE,DE=4cm,BC=8cm$ and area of $△FDE=25c{m}^2$. What is the area of $\Delta ABC$?

• A. 144 cm${}^2$
• B. 121 cm${}^2$
• C. 100 cm${}^2$
• D. 81 cm${}^2$

Answer 1

Answer: (C)

100 cm${}^2$

$DE=4cm,BC=8cm$ and $ar\left(△FDE\right)=25c{m}^2$ [ Given ]

$\Rightarrow$ $△ABC\sim △FDE$ [ Given ]

$\Rightarrow$ $\frac{ar\left(△ABC\right)}{ar\left(△FDE\right)}=\frac{(BC{)}^2}{(DE{)}^2}$ [ By area of similar triangle theorem ]

$\Rightarrow$ $\frac{ar\left(△ABC\right)}{25}=\frac{(8{)}^2}{(4{)}^2}$

$\Rightarrow$ $ar\left(△ABC\right)=\frac{64}{16}\times 25$

$\Rightarrow$ $ar\left(△ABC\right)=4\times 25$

$\therefore$ $ar\left(△ABC\right)=100c{m}^2$