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mote1985 [20]
3 years ago
7

A beach has to enclose a rectangular area, because some endangered species are nesting there. They have 200 feet of rope to rope

off the area with. What is the maximum area that they can rope off?
Mathematics
1 answer:
kkurt [141]3 years ago
6 0
Area is equal to length times width. The perimeter (the amount of rope) has to equal twice the length added to twice the width so we're left with:
A = l * w
200 = 2l + 2w
solve for either l or w
l = 100 - w
plug into the area equation to get one equation with two variables
A = w(100 - w)
A = -w^2 + 100w
take the derivative
A' = -2w + 100
set the derivative equal to zero
0 = -2w + 100
2w = 100
w = 50
This is the width that maximizes the area
with a width of 50, the length must also be 50 to have a perimeter of 200
therefore, they can rope up to 50 * 50 = 2500 ft^2
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There are 12 ways he can pay this amount using the notes he has the answer is 12.

<h3>What are permutation and combination?</h3>

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

Let x be the number of Rs10 notes and y be the Rs20 note

10x + 20y = 220

The whole number of x and y which satisfy the above equation:

x = 0, y =11

x = 2, y =10

x = 4, y =9

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