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Sophie [7]
2 years ago
5

Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 70 feet of fencing to

go around​ it, what dimensions will give him the maximum area in the​ garden? Round the answers to the nearest tenth.
Mathematics
1 answer:
viktelen [127]2 years ago
7 0

The dimension that would give the maximum area is 20.8569

<h3>How to solve for the maximum area</h3>

Let the shorter side be = x

Perimeter of the semi-circle is πx

Twice the Length of the longer side

[70-(\pi )x -x]

Length = [70-(1+\pi )x]/2

Total area =

area of rectangle + area of the semi-circle.

Total area =

x[[70-(1+\pi )x]/2] + [(\pi )(x/2)^2]/2

When we square it we would have

70x +[(\pi /4)-(1+\pi)]x^2

This gives

70x - [3.3562]x^2

From here we divide by 2

35x - 1.6781x^2

The maximum side would be at

x = 35/2*1.6781

This gives us 20.8569

Read more on areas and dimensions here:

brainly.com/question/19819849

#SPJ1

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