A landscape designer has to construct a rectangular flower bed with a perimeter of 100 feet and the maximum possible area. What
1 answer:
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Answer:
625 square feet
Step-by-step explanation:
The greatest area of a polygon with a given perimeter is that of a regular polygon. A regular rectangle is one that has all sides the same length -- a square. The side length of a square with 100 ft perimeter is 25 ft. The area of a square with such a side length is
A = (25 ft)² = 625 ft²
The maximum possible area is 625 ft².
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In the attached, x is the length of one side. The area versus side length is plotted. The maximum is seen to be 625 ft² for a side length of 25 ft.
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We know that
• The radius is 17 feet.
First, we find the circular area
This means the square flower bed will have an area of 615.44 square feet. So, we find its sides with the formula for squared areas