Question

The area of a rectangle is 42 ft', and the length of the rectangle is 5 ft more than double the width. Find the dimensions of the rectangle.

Length: Ift

Answer 1

Length of the rectangle is 12 ft and width is 3.5 ft

Explanation:

• Step 1: Given the Area of the rectangle = 42 ft. Let the width be x, then the length is 5 + 2x. Area of the rectangle = length × width

⇒ 42 = (5 + 2x)x

⇒ 42 = 5x + 2x²

⇒ 2x² + 5x - 42 = 0

⇒ 2x² + 12x - 7x - 42 = 0

⇒ 2x(x + 6) - 7(x + 6) = 0

⇒ (2x - 7)(x + 6) = 0

∴ x = -6, 7/2 (ignore the negative value)

⇒ Width is 3.5 ft

∴ Length is 5 + 2 × 3.5 = 12 ft