Question

The area of a rectangle is 120 square centimeters. If the perimeter is 52 centimeters, find the length and width of the rectangle.

Answer 1

Solution :-

Given : Area of rectangle = 120 cm²

Perimeter = 52 cm

Let the length and breadth of the rectangle be x and y respectively.

According to the question,

xy = 120 _______(i)

2(x + y) = 52

=> x + y = 52/2

=> x = 26 - y ______(ii)

Putting the value of x in equation (i) we get,

(26 - y)y = 120

=> 26y - y² = 120 = 0

=> y² - 26y + 120 = 0

=> y² - 20y - 6y + 120 = 0

=> y(y - 20) - 6(y - 20) = 0

=> (y - 6)(y - 20) = 0

=> y = 6 or  20

Putting the value of y in equation (ii) we get,

=> x = 26 - 6 or x = 26 - 20

=> x = 20 or 6

Hence,

Length = 20 cm

Breadth = 6 cm