Question 902225
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 garden + the area of the walkway) by adding the two areas together.
The area of the garden is :{{{12 * 16 = 192}}}ft^2
Now we will added the two given areas together to find the total area of the garden and the walkway.
192ft^2 + 165ft^2 = 357ft^2
Now we need to write the equation of the area of the large rectangle.
Let X be the width of the walkway.
The new length: {{{L = X + 12 + X}}}
The new width: {{{W = X + 16 + X}}}
The new area equation is:
{{{357 = (X + 12 + X) * (X + 16 + X)}}}
Combine like terms
{{{357 = (2X + 12) * (2X + 16)}}}
Use FOIL to simplify the right hand side of the equation.
*[invoke foil "(2X+12)(2X+16)"]
Rewrite the equation
{{{357 = 4X^2 + 56X + 192}}}
Subtract 357 from both sides
{{{ 0 = 4X^2 + 56X - 165}}}
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