SOLUTION: This is from Activity Bank, INTEGRATED MATHEMATICS 1 Copyright by Houghton Mifflin Company. The city of Casablanca, Morocco has the world's largest swimming pool. The distance

Click here to see ALL problems on Quadratic Equations

Question 196132: This is from Activity Bank, INTEGRATED MATHEMATICS 1 Copyright by Houghton Mifflin Company.
The city of Casablanca, Morocco has the world's largest swimming pool. The distance between two opposite corners of the pool is about 1590 ft. The length is about 1325 ft. longer than the width. What are the length and width of the pool?
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The distance between two opposite corners of the pool is about 1590 ft. The length is about 1325 ft. longer than the width. What are the length and width of the pool?
.
Because the pool is rectangular you can apply Pythagorean theorem:
.
Let w = width
then
w+1325 = length
.
w^2 + (w+1325)^2 = 1590^2
w^2 + (w+1325)(w+1325) = 1590^2
w^2 + (w^2+2650w+1755625) = 2528100
2w^2 + 2650w + 1755625 = 2528100
2w^2 + 2650w - 772475 = 0
Solving using the quadratic equation yields:
w = {245.87, -1570.87}
We can throw out the negative solution leaving:
w = 245.87 feet (width)
.
length:
w+1325 = 245.87+1325 = 1570.87 feet (length)
.
Details of quadratic follows:

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=13202300 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 245.874234553138, -1570.87423455314. Here's your graph: