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02-09-2017
Mathematics

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The perimeter of a rectangle is 44 inches, and its area is 105 square inches. find the length and width of the rectangle.

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APAgony APAgony

02-09-2017

Perimeter = (Length + Width)x2
Area = LengthxWidth

P=(L+W)x2
P/2=L+W
L=P/2 - W

Area=(P/2 - W)(W)
A=WP/2-W^2
105=W(44)/2 - W^2
105=22W - W^2
W^2-22W+105=0
(W-7)(W-15)=0
Width= 7 or 15

A=LxW
105=Lx7
105/7=L
L=15

Length is 15 inches, Width is 7 inches.

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