Question

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.

Answer 1

The dimension that would give the maximum area is 20.8569

How to solve for the maximum area

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