Question

a boardwalk that is x feet wide is built around a rectangular pond. the pond is 30 feet wide and 40 feet long. the combined area of the pond and the boardwalk is 2000 square feet. what is the width of the boardwalk? 5 feet 35 feet 10 feet 40 feet

Explanation:

Step1: Find the length and width of the combined area

The width of the combined area is \(30 + 2x\) (original width \(30\) plus \(x\) on each side). The length of the combined area is \(40+2x\) (original length \(40\) plus \(x\) on each side).

Step2: Set up the area equation

The area of a rectangle is \(A=\text{length}\times\text{width}\). So \((30 + 2x)(40+2x)=2000\).
Expand the left - hand side:

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Divide the entire equation by \(4\).

Step3: Solve the quadratic equation

We can also use the quadratic formula \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\) for the quadratic equation \(ax^{2}+bx + c = 0\). Here \(a = 1\), \(b = 35\), \(c=-200\).

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We have two solutions: \(x=\frac{-35 + 45}{2}=\frac{10}{2}=5\) and \(x=\frac{-35-45}{2}=\frac{-80}{2}=-40\). Since \(x\) represents a width, \(x>0\).

Answer:

5 feet