Question

A rectangle with area of 125cm^2 has sides in the ratio 4:5. What is the perimeter

of the rectangle?

Answer 1

45 cm

Explanation:

The area of a rectangle can be found by multiplying its breadth and width together.

Since the length of the rectangle is usually taken to be the longer side of the rectangle, we can assume that the ratio of the measure of the breadth to its length is 4:5.

Let the breadth of the rectangle be 4 units, where units shall be written as 'u' for simplification.

Thus, the length of the rectangle is 5u.

Area= length ×breadth

125 cm²= (4u)(5u)

125 cm²= 20u²

Divide both sides by 20:

u²= 6.25 cm²

Square root both sides:

u= 2.5 cm

Length= 5(2.5)= 12.5 cm

Breadth= 4(2.5)= 10 cm

The perimeter is the sum of the length of all its sides, i.e. 2(length +breadth).

Perimeter of the rectangle

= 2(12.5 +10)

= 2(22.5)

= 45 cm