<PRE><B>Question 258241</B>
Let x = side of one square
Let y = side of the other square
;
Write an equation for each phrase
:
a 16 inch wire cut into two pieces bent into squares
4x + 4y = 16
simplify, divide by 4
x + y = 4
x = (4-y)
:
find the length if the sum of the areas is 10 in squared
x^2 + y^2 = 10
Replace x with (4-y)
(4-y)^2 + y^2 = 10
FOIL
16 - 8y + y^2 + y^2 = 10
Arrange as a quadratic equation
2y^2 - 8y + 16 - 10 = 0
2y^2 - 8y - 6 = 0
Simplify divide by 2
y^2 - 4y + 3 = 0
Factor
(y - 1)(y - 3) = 0
Two solutions
y = 1, then x = 3
y = 3, then x = 1
;
;
Check:
 4(1) + 4(3) = 16
3^2 + 1^2 = 10

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