SOLUTION: A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.

Algebra.Com
Question 148764: A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.

Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.
.
Let w = width of parking lot
then
w+50 = length of parking lot
.
Using Pythagorean theorem:
w^2 + (w+50)^2 = 250^2
w^2 + (w^2 + 100w + 2500) = 62500
2w^2 + 100w + 2500 = 62500
2w^2 + 100w - 60000 = 0
w^2 + 50w - 30000 = 0
.
If it is too difficult factor, use the "quadratic equation".
You'll get two solutions:
150, -200
.
since it can't negative:
width=150 ft
length = 200 ft
.
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=122500 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 150, -200. Here's your graph:
RELATED QUESTIONS

A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of... (answered by Prithwis)
A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of... (answered by Prithwis)
A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of... (answered by Prithwis)
A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of... (answered by venugopalramana,abdikaidr_jibril@yahoo.com)
A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of... (answered by checkley77)
A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of... (answered by checkley77)
A rectangular parking lot is 50 ft longer than it is wide. Determne the dimensions of the (answered by dolly)
Solve the following problems involving applications of polynomials A rectangular... (answered by vleith)
Hate word problems please help? A rectangular parking lot is 50 ft longer than it is... (answered by stanbon)