SOLUTION: a piece of wire is 52 feet long. it is cut into two pieces, each of which is then bent to form a square. the total are of the square is 97 square feet. how much longer is a side of
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-> SOLUTION: a piece of wire is 52 feet long. it is cut into two pieces, each of which is then bent to form a square. the total are of the square is 97 square feet. how much longer is a side of
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Question 237051: a piece of wire is 52 feet long. it is cut into two pieces, each of which is then bent to form a square. the total are of the square is 97 square feet. how much longer is a side of the larger square then a side of the smaller square? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! piece of wire is 52 feet long. it is cut into two pieces, each of which is then bent to form a square.
the total area of the square is 97 square feet.
how much longer is a side of the larger square then a side of the smaller square?
:
Let x = the side of the large square
Let y = the side of the small square
:
4x + 4y = 52
Divide by 4
x + y = 13
y = (13-x)
and
x^2 + y^2 = 97
Replace y with (13-x)
x^2 + (13-x)^2 = 97
FOIL
x^2 + 169 - 26x + x^2 = 97
Arrange as a quadratic equation
x^2 + x^2 - 26x + 169 - 97 = 0
2x^2 - 26x + 72 = 0
Simplify, divide by 2
x^2 - 13x + 36
Factors to:
(x-9)(x-4) = 0
Two solutions
x = 4
x = 9' The larger side, then 4' is the shorter side
:
The longer side is 5' longer than the shorter side
;
:
Check this
9^2 + 4^2 = 97
and
4(9) + 4(4) = 52
