# The length of a hall is 5 m more than its breadth.

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