Question

The perimeter of a rectangle is 44 cm. The area of the rectangle is 117 cm2. Find the length of the shorter side of the rectangle.

Answer 1

Answer:

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

As the perimeter of a rectangle is 44, we have

2x + 2y = 44 ......(1)

As the area of the rectangle is 117, we have

xy = 117 ........(2)

Simplifying equation (1), we have

x + y = 22 .......(3)

Solving the following simultaneous equations for x and y.

x + y = 22

x + y = 22xy = 117

Substituting y = 22 - x into xy = 117,we have

x(22 - x) = 117

22x - x^2 = 117

x^2 - 22x + 117 = 0

(x - 9)(x - 13) = 0

So x = 9 or x = 13

Substituting x = 9 into y = 22 - x,we have y = 13.

Substituting x = 13 into y = 22 - x,we have y = 9.

So the dimensions of the rectangle are 9 and 13.

the length of the shorter side of the rectangle is 9cm.

hope this will help u.....