SOLUTION: A 22-ft by 28 ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216 ft^2, how wide is the walkway?

Question 902253: A 22-ft by 28 ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216 ft^2, how wide is the walkway?
Answer by Stitch(470) (Show Source): You can put this solution on YOUR website!
The area of a rectangle is given by the equation A = L*W, where L is the length and W is the width.
We can find the total area of the larger rectangle (The area of the pool + the area of the walkway) by adding the two areas together.
The area of the pool is :ft^2
Now we will added the two given areas together to find the total area of the pool and the walkway.
616ft^2 + 216ft^2 = 832ft^2
Now we need to write the equation of the area of the new large rectangle.
Let X be the width of the walkway.
The new length:
The new width:
The new area equation is:

Combine like terms

Use FOIL to simplify the right hand side of the equation.
ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'foil'.

Error occurred executing solver 'foil' .

Rewrite the equation

Subtract 832 from both sides

Now use the quadratic equation to solve for X.

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=5776 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.5, -16.5. Here's your graph:

X = 2.5 & -16.5
Now since we can not have a negative distance -16.5ft will not work for this problem.
So the width of the walkway is 2.5ft
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