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
