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Chapter 2: Problem 80

The perimeter of a rectangle is 180 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 800 square feet.

Short Answer

Expert verified
The possible lengths for the sides could range with balance between length and width due to a fixed perimeter of 180 feet, but they need to be adjusted such that the area doesn't exceed 800 square feet.

Step by step solution

01

Write down the formulas

Write down the formulas for the perimeter and area of a rectangle, which are \(2*(length+width) = perimeter\), and \(length * width = area\).
02

Determine possible lengths

Determine the lengths of a side using the given perimeter of 180 feet. For example, the length and width could be 45 as a starting point because \(2*(length+width) = 2*(45+45) = 180\). However, calculate the area with this length and width, if the area exceeds 800 square feet, reduce the length and width, if not, increase.
03

Check for Maximum Area

Check to see that none of your rectangle dimensions give you an area greater than 800 square feet. If it does, revise your dimensions.
04

Finalize lengths

Finalize all possible lengths and widths that meet the criteria of not exceeding an area of 800 square feet and having a perimeter of 180 feet.

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