A cabinet door has a perimeter of 76 inches. Its area is 357 square inches. What are the dimensions of the door?
1 answer:
Answer:
17 by 21 inches
Step-by-step explanation:
The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...
L + W = 38
LW = 357
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Solution:
W(38 -W) = 357 . . . . . substitute for L
-(W^2 -76W) = 357 . . expand on the left
-(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square
(W -19)^2 = 4 . . . . . . . write as a square
W -19 = ±√4 = ±2 . . . take the square root; next, add 19
W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other
The dimensions are 17 by 21 inches.
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