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

Algebra ->  Test -> 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      Log On


   

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) About Me  (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: X%5E2+%2B+Y%5E2+=+89
Equation 2: X+%2B+3+=+Y
----------------------------------
Substitute (X + 3) into equation 1 for Y.
Equation 1: X%5E2+%2B+Y%5E2+=+89
X%5E2+%2B+%28X+%2B+3%29%5E2+=+89
Rewrite the equation
X%5E2+%2B+%28X%2B3%29%2A%28X%2B3%29+=+89
Simplify the equation
X%5E2+%2B+X%5E2+%2B+3X+%2B+3X+%2B+9+=+89
Combine like terms
2X%5E2+%2B+6X+%2B+9+=+89
Subtract 89 from bith sides
2X%5E2+%2B+6X+-+80+=+0
Use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aX%5E2%2BbX%2Bc=0 (in our case 2X%5E2%2B6X%2B-80+=+0) has the following solutons:

X%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A2%2A-80=676.

Discriminant d=676 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+676+%29%29%2F2%5Ca.

X%5B1%5D+=+%28-%286%29%2Bsqrt%28+676+%29%29%2F2%5C2+=+5
X%5B2%5D+=+%28-%286%29-sqrt%28+676+%29%29%2F2%5C2+=+-8

Quadratic expression 2X%5E2%2B6X%2B-80 can be factored:
2X%5E2%2B6X%2B-80+=+2%28X-5%29%2A%28X--8%29
Again, the answer is: 5, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B6%2Ax%2B-80+%29


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: X+%2B+3+=+Y
5+%2B+3+=+Y
highlight%288+=+Y%29
So the two sides are 5cm & 8cm