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
