Algebra Word Problem?

First, make the first length of wire x and the second one 16 - x. Now convert the words to mathematical expressions. Since the two lengths of wire are bent to make squares, that must mean that they are bent into 4 equal portions. The portion of the first length is x/4 and the portion for the second length is (16 - x)/4).

When the length of one of these portions is squared, that gives you the area of a square. The sum of the areas of the two squares is 10. Set it up like this:

(x/4)^2 + ((16 - x)/4)^2 = 10

Now try to solve for x. First square the things inside the parenthesis,

(x^2/16) + ((256 - 32x + x^2)/16) = 10

You can combine the expressions because they have a common denominator of 16.

(2x^2 - 32x + 256)/16 = 10

Multiply both sides by 16 to cancel it out.

2x^2 - 32x + 256 = 160

Subtract 160 from both sides to get a quadratic equation.

2x^2 - 32x + 96 = 0

Factor out a 2 to make factoring the quadratic easier.

2(x^2 - 16x + 48) = 0

Now factor the quadratic and cancel out the 2 by dividing it.

(x - 12)(x - 4) = 0

x = 12, x = 4

The lengths of the two wires are 12 inches and 4 inches.

Hope this helped!

pieces are 12 inches and 4 inches giving squares of 3 inch side and 1 inch side and areas 9 inch^2 and 1 inch^2 the sum being 10 inch^2.