Question

The length of a hall exceeds its breadth by $8m$ and its area is $180m^2$. Find the perimeter

Answer 1

Let $x$ be the breadth of hall. Then, $x+8$ will be its length.

$l=(x+8)m$ and $b=xm$

$\Rightarrow$ Area of hall $=180m^2$

$\Rightarrow$ $l\times b=180$

$\Rightarrow$ $(x+8)\times x=180$

$\Rightarrow$ $x^2+8x-180=0$

$\Rightarrow$ $x^2+18x-10x-180=0$

$\Rightarrow$ $x(x+18)-10(x+18)=0$

$\Rightarrow$ $(x+18)(x-10)=0$

$\therefore$ $x=10$

$l=x+8=10+8=18m$ and $b=10m$

$\Rightarrow$ Perimeter of hall $=2(l+b)$

$=2(18+10)$

$=2\left(28\right)$

$=56m$