SOLUTION: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path? Give your answ

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Question 67543: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path? Give your answer in decimal form, rounded to the nearest thousandth.

Answer by aaaaaaaa(138)   (Show Source): You can put this solution on YOUR website!
The area of a rectangle is calculated as length times width.
To calculate the area of the garden less area of x width edge, we just subtract x from both the length and width and calculate the area of the smaller rectangle. In algebrese, that is:

As we know that equals 400, we have an equation!




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=1700 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 45.6155281280883, 4.3844718719117. Here's your graph:


As the path cannot be longer than the width of the garden, 20 ft, the width of the path must be approximately 4.38 ft.

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