Asked by Ally
A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. The length of the deck is to be expanded by 10 feet, and the width by 6 feet. If the area of the new rectangular deck is 128 ft^2 larger than the area of the original deck, find the dimensions of the original deck.
Answers
Answered by
Henry
Length = L1.
Width = L1/4.
L2 = L1+10.
W2 = L1/4 + 6.
A2 = A1 + 128 Ft^2.
A2 = (L1*L1/4) + 128.
L2*W2 = (L1*L1/4) + 128.
(L1+10)*(L1/4) + 6) = (L1*L1/4)+128.
Multiply both sides by 4:
(L1+10)*(L1)+24 = (L1*L1) + 512.
L1^2+10L1+24 = L1^2 + 512.
L1^2 - L1^2 + 10L1 + 24 = 512.
10L1 = 512-24 = 488.
L1 = 48.8 Ft.
W1 = L1/4 = 48.8/4 = 12.2 Ft.
Width = L1/4.
L2 = L1+10.
W2 = L1/4 + 6.
A2 = A1 + 128 Ft^2.
A2 = (L1*L1/4) + 128.
L2*W2 = (L1*L1/4) + 128.
(L1+10)*(L1/4) + 6) = (L1*L1/4)+128.
Multiply both sides by 4:
(L1+10)*(L1)+24 = (L1*L1) + 512.
L1^2+10L1+24 = L1^2 + 512.
L1^2 - L1^2 + 10L1 + 24 = 512.
10L1 = 512-24 = 488.
L1 = 48.8 Ft.
W1 = L1/4 = 48.8/4 = 12.2 Ft.
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