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A carpenter is assigned the job of expanding a rectangular deck where the length is three times the width. The width of the deck is to be expanded by 8 feet and the length is to be expanded by the new width. If the area of the new rectangular deck is 240 ft larger than the area of the original deck, find the dimensions of the original deck.

Question

26-03-2021
Mathematics

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URGENT!! YOU WILL GET BRAINLIEST!

A carpenter is assigned the job of expanding a rectangular deck where the length is three times the width. The width of the deck is to be expanded by 8 feet and the length is to be expanded by the new width. If the area of the new rectangular deck is 240 ft larger than the area of the original deck, find the dimensions of the original deck.

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PurpleOcean PurpleOcean · Answer 1 · 2021-03-26T00:53:52+01:00

Let Xo = original length of the deck
Yo = original width of deck
Therefore:
Yo = (1/6)Xo
The original deck area is:
Ao = XoYo
Ao = Xo(1/6)Xo = (1/6)Xo2
The length of the new deck is 4ft longer than the original deck, or XN = Xo + 4, and the width is 2ft longer than the original, or YN = Yo + 2, and the new area of the deck is 56ft2 than the original area, or AN = Ao + 56.
Therefore: AN = XNYN
Ao + 56 = (Xo + 4)(Yo + 2)
(1/6)Xo2 + 56 = (Xo + 4)(1/6Xo + 2)
(1/6)Xo2 + 56 = (1/6)Xo2 + 2Xo + (4/6)Xo +8
56 = 2Xo + (2/3)Xo +8
56 - 8 = (2 + 2/3)Xo
48 = (6/3 + 2/3)Xo
48 = (8/3)Xo
48(3/8) = Xo
Xo = 18ft
Yo = (1/6)(18)
Yo = 3ft
Check: Ao = XoYo = (18)(3) = 54ft2
XN = Xo + 4 = 18 + 4 = 22ft
YN = Yo + 2 = 3 + 2 = 5ft
AN = (22)(5) = 110ft2
Ao + 56 = AN
54 + 56 = 110
110 = 110 check------->ANSWER: original length, Xo = 18ft
original width, Yo = 3ft