#### 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}, what are the length and breadth of the hall?

#### Solution

Let the breadth of the rectangular hall be x meters and the length = (x + 5) meters Then

And area of the rectangle

length x breadth = 84

(x + 5)x = 84

x2 + 5x - 84 = 0

x2 - 7x + 12x - 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 meters and length be 12 meters.

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#### APPEARS IN

Solution The Length of a Hall is 5 M More than Its Breadth. If the Area of the Floor of the Hall is 84 M2, What Are the Length and Breadth of the Hall? Concept: Solutions of Quadratic Equations by Factorization.