Question 404199: a wire of length 100 cm is cut into two piece and each part is bent to form a square. if the sum of the areas of the two square is 425 cm^2 find the lenghts of the sides of the two squares
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a wire of length 100 cm is cut into two piece and each part is bent to form a square.
if the sum of the areas of the two square is 425 cm^2 find the lengths of the sides of the two squares
:
Let x = side of one square
Let y = side of the other square
then
4x + 4y = 100
simplify, divide by 4
x + y = 25
y = (25-x), use this for substitution
and
x^2 + y^2 = 425
Substitute (25-x) for y
x^2 + (25-x)^2 = 425
FOIL (25-x)(25-x)
x^2 + 625 - 50x + x^2 = 425
Arrange as a quadratic equation
x^2 + x^2 - 50x + 625 - 425 = 0
2x^2 - 50x + 200 = 0
(x-20)(2x-10) = 0
Two solutions
x = 20 is the side of one square
or
2x = 10
x = 5 is the side of one square
:
Find y
25 - 20 = 5 is the side of the other square
or
25 - 5 = 20 is the side of the other square
:
anyway, one square side is 20, the other square side is 5
:
:
See if this is true
4(20) + 4(5) =
80 + 20 = 100
and
20^2 + 5^2 = 425
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