SOLUTION: A piece of wire having a total length of 72 cm was cut into two unequal segments and bent to form two unequal squares. If the total area of the squares is 180-sq.cm.,what is the di

We start with this 72 cm piece of wire



Now we cut it into two unequal parts like this:

 

Now we bend each piece into a square:

 

Now we label each side of the first square x and each side of
the second square y:

 

Each square has 4 sides, so the perimeter of the first square is 4x,
and the perimeter of the second square is 4y, and we know the sum of
all their sides total up to the length of the original wire, or 72 cm.
So we have the equation:

4x + 4y = 72

The area of the first square is x², and the area of the second square
is y² and we are told that the sum of their areas is 180. So we also 
have this equation:

x² + y² = 180
 
So we have
the system of equations:

4x + 4y = 72
x² + y² = 180

Can you solve these? Solve the first equation
for y and substitute it in the second equation.
Then you have a quadratic equation.  You get
x = 12, x = 6

Then substitute these in the first equation
and get
y = 6, y = 12

So there seem to be two solutions,

(x,y) = (12,6) and (x,y) = (6,12)

but the first is just the case when the bigger
square is on the left and the second case is
the same except the smaller square is on the left.

So the way I have the picture drawn, the big piece
of wire is the sum of the 4 sides of the big square
or 12×4 or 48 cm and the sum of the 4 sides of the
little square is 6×4 or 24 cm.  So the difference
between the pieces of wire is 48-24 or 24 cm.

Edwin