Question

The perimeter of a rectangle is 100 and its diagonal has length x. The area of this rectangle is.

• A. $625-x^2$
• B. $625-\frac{x^2}{2}$
• C. $1250-x^2$
• D. $1250-\frac{x^2}{2}$

Answer 1

Answer: (D)

$1250-\frac{x^2}{2}$

Perimeter of rectangle = $2(\ell +b)$
$2(\ell +b)=100$
$\ell +b=50$ ....(i)
Diagonal of Rectangle = $\sqrt{{\ell }^2+b^2}$
x=$\sqrt{{\ell }^2+b^2}$
$x^2={\ell }^2+b^2$
Taking the square of equation (i)
$(\ell +b{)}^2=(50{)}^2$
${\ell }^2+b^2+2\ell b=2500$
$x^2+2\ell b=2500$
$2\ell b=2500-x^2$
$\ell b=\frac{2500-x^2}{2}$ or $\ell b=1250-\frac{x^2}{2}$
Area of rectangle = $1250-\frac{x^2}{2}$.