SOLUTION: If two opposite sides of a square are increased by 9 meters and the other sides are decreased by 6 meters, the area of the rectangle that is formed is 78 square meters. Find the a

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Question 103385: If two opposite sides of a square are increased by 9 meters and the other sides are decreased by 6 meters, the area of the rectangle that is formed is 78 square meters. Find the area of the original square.
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
let x=original sides of the square.
A=L*W
(x+9)(x-6)=78
x^2+3x-54=78
x^2+3x-132=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=537 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 10.0866302262565, -13.0866302262565. Here's your graph:

The area of the original square=(10.0866...)= 101.74 sq meters
Ed


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