SOLUTION: A piece of wire 64 centimeters in length is cut into two parts. Each part is then bent to form a square.The total area of the two squares is 130 square centimeters.
How much longe
Algebra ->
Customizable Word Problem Solvers
-> Geometry
-> SOLUTION: A piece of wire 64 centimeters in length is cut into two parts. Each part is then bent to form a square.The total area of the two squares is 130 square centimeters.
How much longe
Log On
Question 265430: A piece of wire 64 centimeters in length is cut into two parts. Each part is then bent to form a square.The total area of the two squares is 130 square centimeters.
How much longer is a side of the larger square than a side of the smaller square?
You can put this solution on YOUR website! A piece of wire 64 centimeters in length is cut into two parts.
Each part is then bent to form a square.
The total area of the two squares is 130 square centimeters.
How much longer is a side of the larger square than a side of the smaller square?
:
Let x = side of one square
Let y = side of the other square
:
"A piece of wire 64 centimeters in length is cut into two parts."
4x + 4y = 64
simplify, divide by 4
x + y = 16
y = (16-x); for substitution
:
"The total area of the two squares is 130 square centimeters."
x^2 + y^2 = 130
:
x^2 + (16-x)^2 = 130; substituted for y
:
x^2 + (256 - 32x + x^2) = 130
:
2x^2 -32x + 256 - 130 = 0
:
2x^2 - 32x + 126 = 0
Simplify, divide by 2
x^2 - 16x + 63 = 0
Factor
(x-9)(x-7) = 0
Two solutions
x = 9; then y = 7
x = 7; then y = 9
:
"How much longer is a side of the larger square than a side of the smaller square?"
We can confidently say 2 cm
:
:
Check 9^2 + 7^2 = 130 and 4(9) + 4(7) = 64
