Question

A wall is rectangular in shape, has a perimeter of 72m. If the length of its diagonal is 18m, what is the area of the wall?

• A.
  $224m^2$
• B.
  $486m^2$
• C.
  $572m^2$
• D.
  $606m^2$

Answer 1

The correct option is B

$486m^2$



$Perimeter=72m$

$\Rightarrow (a+b)\times 2=72m..........\left(i\right)$
$a+b=36m$

$a^2+b^2=c^2$
$\Rightarrow a^2+b^2={18}^2=324.........\left(ii\right)$

$Area=a\times b.........\left(iii\right)$

$Weknow,(a+b{)}^2=a^2+b^2+2ab$

$\Rightarrow {36}^2=324+2\times \text{(}Area)$

$\Rightarrow \text{(}Area)=486m^2$