Question:
The length of a hall is $5 \mathrm{~m}$ more than its breadth. If the area of the floor of the hall is $84 \mathrm{~m}^{2}$, what are the length and breadth of the hall?
Solution:
Let the breadth of the rectangular hall be $=x$ metres and the length $=(x+5)$ metres Then
And area of the rectangle
length $\times$ breadth $=84$
$(x+5) x=84$
$x^{2}+5 x-84=0$
$x^{2}-7 x+12 x-84=0$
$x(x-7)+12(x-7)=0$
$(x-7)(x+12)=0$
$(x-7)=0$
$x=7$
or
$(x+12)=0$
$x=-12$
Sides of the rectangular hall never are negative.
Therefore, length
$=(x+5)$
$=7+5$
$=12$
Hence, breadth of the hall be 7 metres and length be 12 metre