The length of a rectangle is 8 feet more than it's width. The area of the rectangle is 84 square feet. Find it's length and width.

Length of the rectangle is 14 ft and width is 6 ft

Step-by-step explanation:

Step 1: Let the width of the rectangle be x, then length = 8 + x. Find dimensions if area = 84 ft²

⇒ Area of the rectangle = length * width

⇒ 84 = x (8 + x) = 8x + x²

⇒ x² + 8x - 84 = 0

⇒ x² + 14x - 6x - 84 = 0 (Using product sum rule to factorize)

⇒ x (x + 14) - 6 (x + 14) = 0

⇒ (x + 14) (x - 6) = 0

⇒ x = - 14, + 6 (negative value is neglected)

∴ x = 6 and x + 8 = 14