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 widt

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3 years ago

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1 answer:

S_A_V [24] · Answer 1 · 2022-05-12T05:05:35+03:00

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