Steven has 100 ft. of fencing and wants to use it all to enclose a garden area. He wants the area to have the largest area possible. What will the perimeter of the garden be?
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2007-12-31 15:10:18 · 5 answers · asked by ♥♪Kelly♪♥ 1 in Science & Mathematics ➔ Mathematics
100ft is the perimeter. they are tricking you with useless info.
100ft will be permiter because that is how much material steven has.
2007-12-31 15:14:28 · answer #1 · answered by Anonymous · 2⤊ 0⤋
It can be proved by calculus that the maximum area that can be contained within a given perimeter is a circle if you have unlimited sides, or a square if you have four sides.
Thus, the maximum area inside a 100-ft perimeter square is 25 X 25 = 625 square feet.
If you can have any number of sides, use an infinite number of sides to get a circle.
The answer is a circle with a circumference of 100 feet.
2007-12-31 23:19:21 · answer #2 · answered by MVB 6 · 0⤊ 0⤋
The perimeter of the garden will be 100 feet because that's how much fence he has.
a circle maximizes the area with a given amount of fence
A = pi*r^2
C = 2pi*r
100 = 2pi*r
r = 50/pi
A = pi*(50/pi)^2 = 2500/pi
2007-12-31 23:17:44 · answer #3 · answered by Steve A 7 · 0⤊ 0⤋
Largest area fenced with 100 ft fence is 625 sq ft as square is the largest of quadrilaterals with given perimeter.
100 ft / 4 = 25 ft side of square and area = (25ft)^2 = 625 ft^2
If garden can be circular then it will be larger than square and
its area = 804.352 ft^2 where its circumference 2(3.142)r = 100 and area 3.142r^2 = 3.142(100/2*3.142)^2 = 804.352
2007-12-31 23:16:19 · answer #4 · answered by sv 7 · 0⤊ 1⤋
too late for me to think properly, but i think you use Dy/dx, d2y/dx2 and d3y/dx3 to find max value.
2007-12-31 23:15:08 · answer #5 · answered by Anonymous · 0⤊ 1⤋