Question 902253
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 :{{{22 * 28 = 616}}}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: {{{L = X + 22 + X}}}
The new width: {{{W = X + 28 + X}}}
The new area equation is:
{{{832 = (X + 22 + X) * (X + 28 + X)}}}
Combine like terms
{{{832 = (2X + 22) * (2X + 28)}}}
Use FOIL to simplify the right hand side of the equation.
*[invoke foil "(2X+22)(2X+28)"]
Rewrite the equation
{{{832 = 4X^2 + 100X + 616}}}
Subtract 832 from both sides
{{{ 0 = 4X^2 + 100X - 216}}}
Now use the quadratic equation to solve for X.
*[invoke quadratic "X", 4,56,-165]
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