The perimeter of a rectangle is 60 cm. Take x as the breadth and express length in terms of x. If the area of a rectangle is 216 centimetre square, find the value of x.

Let the breadth of the rectangle be x.

We konw that,

Perimeter of a rectangle = 2(length + breadth)

→2(length + x) = 60

→length = 30 - x

 

Area of a rectangle = length × breadth = 216  ....  given

→(30 - x)x=216

→ x² - 30x + 216 = 0   

^{→ x2 - 18x - 12x + 216 = 0} 

 ^{→ x(x - 18)-12(x - 18) = 0
→ (x - 18)(x - 12) = 0}

→ x = 18 or x = 12

If breadth is 18cm then length is 12cm and if breadth is 12cm then length is 18cm.