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Neko [114]
3 years ago
7

A large rectangular area is to be fenced off ( a large rectangle divided into 2 smaller rectangles). The fence used to divide th

e space cost $10 per foot and the fence used for the perimeter costs$15 per foot. If the total budget for the project is $60000 what are the dimensions that yield the largest area
Mathematics
1 answer:
Anvisha [2.4K]3 years ago
3 0

Answer:

Length of area is 857.14 ft

Width of area is 857.14 ft

Length of dividing fence is 857.14 ft

Step-by-step explanation:

Here we have

Area of rectangle = Length × Width

The dimension, of the rectangle with the largest area is the dimension of a square, hence we have;

Length of rectangle = Width of rectangle = x

Hence,  the perimeter of the area = 4·x, while the width of the dividing fence = x

Therefore, since the we have;

Cost of the perimeter fence = $15/foot

Cost of the dividing fence = $10/foot

Then;

4·x × 15 + x × 10 = 60000

60·x + 10·x = 60000

x = 60000/70 = 857.14 ft

Which gives the following dimensions;

Length of area = 857.14 ft

Width of area = 857.14 ft

Length of dividing fence = 857.14 ft.

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What is the area of the 50ft by 100ft yard?
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However, in this problem, we also have other shapes in the rectangle. To find the area of JUST the green, we need to subtract the areas of the two circles and small blue rectangle.

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