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
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Question 255251: 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! Let the side of the larger square be x
and the side of the smaller square be y
Perimeter of the larger square =4x
Perimeter of the smaller square =4y
Total length 4x+4y = 64
Dividing by 4, we get x+y = 16
y = 16-x ...(1)
Total area is x^2+y^2 = 130
x^2+(16-x)^2 = 130
x^2+256+x^2-32x-130 = 0
2x^2-32x+126 = 0
x^2-16x+63 = 0
(x-7)(x-9) = 0
x = 9 or x = 7
When x=9, (1)=> y = 16-9 = 7
Therefore the difference between the sides of the larger square
and smaller square = x-y = 9-7 = 2 cm
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