Question

The width of the rectangle is 2/3 of its length. If the perimeter of the rectangle is 80 cm. Find its area.

Answer 1

perimeter of rectangle = 2*length + 2*width

width = (2/3)*length

perimeter = 2 * length + 2*(2/3)*length
perimeter = 80
80 = 2 * length + 2*(2/3)*length
40 = length + (2/3)*length
40 = (5/3)*length
length = 24
width = (2/3)*24 = 16

Area = length * width
Area = 24 * 16 = 384

Answer 2

Given:

The width of the rectangle is 2/3rd of its length. The perimeter of the rectangle is 80 cm.

To Find:

The area of the rectangle is?

Solution:

1. Let the length of the rectangle be l and the width of the rectangle be w.

2. The width of the rectangle is 2/3rd of its length, The algebratic equation will be,

=> width = (2/3) * length,

=> w = (2l/3).

3. The perimeter of the rectangle is 80cm.

=> Perimeter of the rectangle = 2x(length + width),

=> 80 = 2(l+w),

=> 80 = 2 ( l + 2l/3 ),

=> 80 = 2(5l/3),

=> 80 = 10l/3,

=> l = (80x3)/10,

=> l = 8 x 3 = 24 cm.

4. width = (2l/3) = (2x24/3) = 16cm.

5. The area of the rectangle is given by the formula,

=> Area of the rectangle = length x width,

=> Area of the rectangle = 24 x 16,

=> Area of the rectange = 384 cm².

Therefore, the area of the rectangle is 384cm².