Question 969628: The length of a rectangle is 7 inches longer than it is wide. If the area is 120 square inches, what are the dimensions of the rectangle?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Length * width =Area
Length =x
Width = x-7, because the length is longer than wide, and we subtract.
area= x(x-7) and units are in^2 because base units are inches.
x^2-7x=120
subtract 120 from each side
x^2-7x-120=0
Factor using 15 and 8. The 15 must be negative so that the middle term is negative.
(x-15) (x+8)=0
set each =0, because one factor must equal zero for the whole thing to equal zero.
x-15=0; x=15 inches
x+8=0; x= -8 inches. This is impossible, so this root is not used.
The length is 15 inches.
The width is 15-7 or 8 inches.
The area is 15 in * 8 in=120 in^2, which matches the required area.
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