Question

you have 350 feet of fencing to enclose a rectangular plot that borders on a river. if you do not fence the side along the river, find the length and width of the plot that will maximize the area. what is the largest area that can be enclosed?

the width, labeled x in the figure, is 87.5 feet.
(type an integer or decimal.)

the length, labeled \\(350 - 2x\\) in the figure, is 175 feet.
(type an integer or decimal.)

the largest area that can be enclosed is square feet.
(type an integer or decimal.)

Explanation:

Set up the area function

Using the Quadratic Word Problems knowledge point

$$
LATEXBLOCK0
$$

Find the vertex to maximize area

Using the Maximum Value of Quadratic knowledge point

$$
LATEXBLOCK1
$$

Calculate the maximum area

Using the Maximum Value of Quadratic knowledge point

$$
LATEXBLOCK2
$$

Answer:

You have 350 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

The width, labeled x in the figure, is <blank>87.5</blank> feet.
(Type an integer or decimal.)

The length, labeled 350 - 2x in the figure, is <blank>175</blank> feet.
(Type an integer or decimal.)

The largest area that can be enclosed is <blank>15312.5</blank> square feet.
(Type an integer or decimal.)