Question

You want to enclose a rectangular region with an area of 1200 square feet and a length of 40 feet, 50 feet, or 60 feet. Find the perimeter for each possible region. Explain why you might rewrite the area formula to find the solutions.

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Answer 1

To find the perimeters of rectangular regions with a fixed area of 1200 square feet and varying lengths, compute the width by dividing the area by the length, then calculate the perimeter using the formula P=2l + 2w.

Step-by-step explanation:

Calculating Perimeters for Different Rectangular Regions

To find the perimeter of a rectangular region, we can use the formula P=2l+2w, where P is the perimeter, l is the length, and w is the width. You have given an area of 1200 square feet to work with and potential lengths of 40 feet, 50 feet, or 60 feet. Let's calculate the width for each of these options using the area formula A=lw:

1. For a length of 40 feet: width w = 1200 / 40 = 30 feet; perimeter P = 2(40) + 2(30) = 140 feet.
2. For a length of 50 feet: width w = 1200 / 50 = 24 feet; perimeter P = 2(50) + 2(24) = 148 feet.
3. For a length of 60 feet: width w = 1200 / 60 = 20 feet; perimeter P = 2(60) + 2(20) = 160 feet.

We might choose to rewrite the area formula to solve for width in terms of the area and length so we can calculate the perimeter for each given length.