Question

In the given figure, $BC\parallel DE$, area $\left(△ABC\right)=25{cm}^2$,
area (trap. $BCED)=24{cm}^2$ and $DE=14cm$. Calculate the length of $BC$.

• A. $20cm$
• B. $10cm$
• C. $5cm$
• D. $Noneofthese$

Answer 1

The correct option is B $10cm$

Given: $BC\parallel DE$
In $△ABC$ and $△ADE$
$\angle BAC=\angle DAE$ (Common angle)
$\angle ABC=\angle ADE$ (Corresponding angles)
$\angle ACB=\angle AED$ (Corresponding angles)
Thus, $△ABC\sim △ADE$ (AAA rule)
Hence, $\frac{A\left(△ABC\right)}{A\left(△ADE\right)}=\frac{B{C}^2}{D{E}^2}$
$\frac{A\left(△ABC\right)}{A\left(△ABC\right)+A(trap.BCED)}=\frac{B{C}^2}{D{E}^2}$
$\frac{25}{25+24}=\frac{B{C}^2}{D{E}^2}$
$D{E}^2=\frac{14\times 14\times 25}{49}$
$D{E}^2=25\times 4$
$DE=10$ cm