Question

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.

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.