#### Question

The perimeter of a rectangular field is 82 m and its area is 400 m^{2}. Find the breadth of the rectangle.

#### Solution

Let the breadth of the rectangle be x meters. Then

Perimeter = 82 meters

2(length + breadth) = 82

(length + x) = 41

length = 41 - x

And area of the rectangle

length x bradth = 400

(41 - x)x = 400

41x - x^{2} = 400

x^{2} - 41x + 400 = 0

x^{2} - 25x - 16x + 400 = 0

x(x - 25) -16(x - 25) = 0

(x - 25)(x - 16) = 0

or

x - 16 = 0

x = 16

Since perimeter is 82 meter. So breadth can’t be 25 meter.

Hence, breadth 16 meters.

Is there an error in this question or solution?

#### APPEARS IN

Solution The Perimeter of a Rectangular Field is 82 M and Its Area is 400 M2. Find the Breadth of the Rectangle. Concept: Solutions of Quadratic Equations by Factorization.