Question

The perimeter of the rectangular field is 82 m and its area is 400 m². Find the breadth of the rectangle?

Answer 1

Given,

Perimeter = 82 m and its area = 400 m²

Let the breadth of the rectangle be considered as x m.

We know that,

Perimeter of a rectangle = 2(length + breadth)

82 = 2(length + x)

41 = (length + x)

⇒Length = (41 – x)m

We also know that,

Area of the rectangle = length x breadth

400 = (41 – x)(x)

400 = 41x – x²

x² – 41x + 400 = 0

x² – 25x – 16x + 400 = 0

x(x – 25) – 16(x – 25) = 0

(x – 16)(x – 25) = 0

Now, either x – 16 = 0 ⇒ x = 16

Or, x – 25 = 0 ⇒ x = 25

Therefore, the breadth of the rectangle can be either 16 m or 25 m respectively.