Question

The length of a hall is $5$ m more than its breadth. If the area of the floor of the hall is 84 $m^2$, then the sum of length and the breadth is___m

Answer 1

$\Rightarrow$ Let breadth of a hall be $xm$

$\Rightarrow$ Then length of a hall $=(x+5)m$

$\Rightarrow$ Area of a hall $=84m^2$

$\Rightarrow$ $x(x+5)=84$

$\Rightarrow$ $x^2+5x-84=0$

$\Rightarrow$ $x^2+12-7x-84=0$

$\Rightarrow$ $x(x+12)-7(x+12)=0$

$\Rightarrow$ $(x+12)(x-7)=0$

$\therefore$ $x=-12$ or $x=7$

Breadth can not be negative.

$\therefore$ Breadth of a hall $=7m$

$\Rightarrow$ Length of a hall $=x+5=7+5=12m$

$\Rightarrow$ Required sum $=7+12=19m$