A rectangle has an area of 80cm squared and a perimeter of 48cm find the length and width of the rectangle

2 possible solutions.

When width is 4 cm, length is 20 cm; When width is 20 cm, length is 4 cm

Step-by-step explanation:

Step 1: Let the width of the rectangle be x. Perimeter of the rectangle = 48 cm. Find expression for length.

Perimeter of the rectangle = 2 (length + width)

48 = 2 (length + x)

24 = length + x

⇒ Length = 24 - x

Step 2: Find the dimensions if area = 80 cm

Area of the rectangle = length * width

80 = x (24 - x)

80 = 24x - x²

x² - 24x + 80 = 0

x² - 20x - 4x + 80 = 0

x (x - 20) - 4 (x - 20) = 0

(x - 4) (x - 20) = 0

⇒ x = 4, 20

24 - x = 20, 4

So there are two possible answers.

When width is 4 cm, length is 20 cm

When width is 20 cm, length is 4 cm