A carpenter is assigned the job of expanding a rectangular deck where the width is one-sixth the length. The length of the deck is to be expanded by 4 feet, and the width by 2 feet. If the area of the new rectangular deck is 56 ft2 larger than the area of the original deck, find the dimensions of the original deck.

Question

Royce

Mathematics

25 February, 16:49

A carpenter is assigned the job of expanding a rectangular deck where the width is one-sixth the length. The length of the deck is to be expanded by 4 feet, and the width by 2 feet. If the area of the new rectangular deck is 56 ft2 larger than the area of the original deck, find the dimensions of the original deck.

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Cortez Barrera · Answer 1

Let the area of the original deck be x * x/6

new deck will have area (x + 4) * (1/6x + 2)

so we can write the equation

(x + 4) ((1/6) x + 2) - x^2/6 = 56

x^2/6 + 2x + 2x/3 + 8 - x^2/6 = 56

8x / 3 = 48

x = 144/8 = 18

so length of original deck = 18 feet and width = 3 feet.