Question

as part of a recreational waterfront grant, the city council plans to enclose a rectangular area along the waterfront of a lake and create a park and swimming area. the budget calls for the purchase of 10,000 feet of fencing. (note: there is no fencing along the lake.) complete parts a through c below.
images of four figures labeled a, b, c, d

b. write an expression that represents the width (side opposite the water) in terms of x.
an expression that represents the width in terms of x is \boxed{}. (simplify your answer.)

Explanation:

Step1: Identify the total fencing

The total length of fencing available is 10,000 feet.

Step2: Analyze the fencing sides

From the diagram (option D), there are two sides of length \( x \) (the sides perpendicular to the water) and one side (the width, opposite the water) that we need to find. Let the width be \( w \). The total fencing used is the sum of the two \( x \)-sides and the width: \( 2x + w = 10000 \).

Step3: Solve for the width \( w \)

To find \( w \) in terms of \( x \), we rearrange the equation: \( w = 10000 - 2x \).

Answer:

$10000 - 2x$