Question

The area of a rectangle is 20cm2. The perimeter of the rectangle is 18cm. What are the lengths of the side of the rectangle.

Please can you use simultaneous equation method to solve this

Answer 1

Explanation:

Let length = x and width =y

Area of rectangle = 20 square inches

x*y = 20

xy = 20 -------------(I)

Perimeter = 18 cm

2*length + 2*width = 18

2x + 2y = 18

Divide the entire equation by 2

x + y = 9

x = 9 -y -----------------(II)

Substitute x = 9 - y in equation (I)

(9 - y)*y = 20

9y - y² = 20

0 = 20 +y² - 9y

y² - 9y + 20 = 0

y² - 4y - 5y + 20 = 0

y(y - 4) - 5(y - 4) = 0

(y -4)(y -5) = 0

y - 4 = 0 ; y- 5 = 0

y = 4 ; y = 5

Length = 4 cm and width = 5 cm