A cabinet door has a perimeter of 76 inches. Its area is 357 square inches. What are the dimensions of the door?

Mathematics

1 answer:

luda_lava [24]3 years ago

3 0

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

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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