Question 638374: A wire of length 16 inches is to be cut into two pieces; then each piece will be bent to form a square. Find the length of the two pieces assuming that the sum of the areas of the two squares is 10 square inches.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A wire of length 16 inches is to be cut into two pieces; then each piece will be
bent to form a square.
Find the length of the two pieces assuming that the sum of the areas of the two
squares is 10 square inches.
:
Let the length of the sides of the two square be x & y
:
4x + 4y = 16
simplify, divide by 4
x + y = 4
y = (4-x)
and
x^2 + y^2 = 10
:
Replace y with (4-x)
x^2 + (4-x)^2 = 10
FOIL (4-x)(4-x)
x^2 + 16 - 8x + x^2 = 10
Combine like terms on the left
x^2 + x^2 - 8x + 16 - 10 = 0
2x^2 - 8x + 6 = 0
simplify, divide by 2
x^2 - 4x + 3 = 0
Factors to
(x-1)(x-3) = 0
Two solutions
x = 1, then y = 3
and
x = 3, then y = 1
:
:
You can check if this is true in the two original equations
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