SOLUTION: A piece of wire 100 cm long is to be cut into 2 pieces, and those 2 pieces are each to be bent to make a square. The area of one square is to be 225 cm^2 (cm squared) greater than

Question 1026754: A piece of wire 100 cm long is to be cut into 2 pieces, and those 2 pieces are each to be bent to make a square. The area of one square is to be 225 cm^2 (cm squared) greater than the other. What is the sum of the areas of the two squares?
The answer is 353 cm squared, but how did they end up with such answer? The computation is one that I do not get. How can the larger square end up as 25-x and etc?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
side of one square be x
Area = x
side of other square = y
area of square = y^2
sum of perimeters
4x+4y =100
x+y=25....................(1)
Difference between areas
x^2-y^2=225
(x+y)(x-y)=225
but (x+y) =25
(x-y) = 9..................(2)
add (1) & (2)
2x =34
x=17
y=8
sum of areas
x^2+y^2= 17^2+8^2 =353

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