The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is $84\ m^2$, what are the length and breadth of the hall?

Given:

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

The area of the floor of the hall $=84\ m^2$.

To do:

We have to find length and breadth of the hall.

Solution:

Let the length of the rectangular hall be $x$ m and the breadth of the rectangular hall be $y$ m.

This implies,

$x=y+5\ m$

According to the question,

$x \times y=84$

$(y+5)y=84$

$y^2+5y=84$

$y^2+5y-84=0$

Solving for $y$ by factorization method, we get,

$y^2+12y-7y-84=0$

$y(y+12)-7(y+12)=0$

$(y+12)(y-7)=0$

$y+12=0$ or $y-7=0$

$y=-12$ or $y=7$

Length cannot be negative. Therefore, breadth of the hall$=7\ m$.

$x=7+5=12\ m$

The breadth of the hall is $7\ m$ and the length of the hall is $12\ m$.

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Updated on: 10-Oct-2022

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