SOLUTION: the number of inches in the perimeter of a square is 3 more than the number of square inches in its area. find the length of a side.

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Question 547553: the number of inches in the perimeter of a square is 3 more than the number of square inches in its area. find the length of a side.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the length of a side (in inches) is x,
the perimeter of the square (in inches) is 4x,
and the area (in square inches) is x%5E2.
The wording says that 4x is 3 more than x%5E2.
That means 4x=x%5E2%2B3 <--> x%5E2-4x%2B3=0 <--> %28x-1%29%28x-3%29=0, which gives you two solutions: x=1 and x=3.
A square of side 1 inch has an area of 1 square inch and a perimeter of 4 inches, with 4 being 3 more than 1.
A square of side 3 inches has an area of 9 square inch and a perimeter of 12 inches, with 12 being 3 more than 9.
If you graph perimeter=4x and area%2B3=x%5E2%2B3, you find that they cross at two points.
graph%28200%2C300%2C-1%2C4%2C-3%2C15%2C4x%2Cx%5E2%2B3%29