SOLUTION: The sum of the area of two squares is 89 squares centimeters. The lenght of a side of the larger square is 3 cm more than the lenght of a side of the smaller square. Find the dimen

Question 688745: The sum of the area of two squares is 89 squares centimeters. The lenght of a side of the larger square is 3 cm more than the lenght of a side of the smaller square. Find the dimensions of each square.
Answer by Stitch(470) (Show Source): You can put this solution on YOUR website!
Let X = the length of a side on the small square.
Let Y = the length of a side on the large square.
The area of a square is the Length^2
Equation 1:
Equation 2:
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Substitute (X + 3) into equation 1 for Y.
Equation 1:

Rewrite the equation

Simplify the equation

Combine like terms

Subtract 89 from bith sides

Use the quadratic equation.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=676 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5, -8. Here's your graph:

Note that you can not have a negative value for the answer. So X = 5
Now plug 5 into equation 2 for X
Equation 2:

So the two sides are 5cm & 8cm

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