Question

The length of a rectangular field is four times the width of the field. If you have at most 95 feet of fencing, what is the largest width the field can have and still be enclosed by fencing? Complete the inequality that represents the solution set. Write your answer as a decimal rounded to the tenths place.

A) 4w + 2l ≤ 95, where w is the width and l is the length.
B) 2w + 4l ≤ 95, where w is the width and l is the length.
C) 2w + 8l ≤ 95, where w is the width and l is the length.
D) 4w + 8l ≤ 95, where w is the width and l is the length.

Answer 1

To find the largest width the field can have and still be enclosed by fencing, set up an inequality based on the given information: 2w + 8w ≤ 95. The largest width is 9.5 feet.

Step-by-step explanation:

To find the largest width the field can have and still be enclosed by fencing, we need to set up an inequality based on the given information.

The length of the field is four times the width, so we can let the width be represented by w. Therefore, the length is 4w.

The perimeter of a rectangle is given by the formula P = 2w + 2l, where P is the perimeter, w is the width, and l is the length.

Given that the perimeter should be at most 95 feet, we can set up the inequality: 2w + 2(4w) ≤ 95.

Simplifying the inequality gives us 2w + 8w ≤ 95. This simplifies to 10w ≤ 95. Dividing both sides by 10 gives us w ≤ 9.5.

Therefore, the largest width the field can have and still be enclosed by fencing is 9.5 feet.