You have to make a pen using the barn as a side with a perimiter of 144 what is the largest possible area. Exp

Question

Show work need by tonight.

Answer 1

Let W be the width of the pen (2 fences perpendicular to the barn).
Let L be the length of the pen (1 fence parallel to the barn).

We know that 2W + L = 144
Solve for L:
L = 144 - 2W

Now create a function for the area:
Area = W * L
Area = W (144 - 2W)
Area = -2W² + 144W

If you take the first derivative and set it to zero you get:
-4W + 144 = 0
4W = 144
W = 36

Thus the area will be maximized when the width is 36 and the length is 72.

Answer 2

The Square

A = s²

Since the square have four sides

The sides equal 3 x 4 = 12

144 = 12²

144 = 144

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The largest possible area for a square is

3 times 4 = 12²

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The rectangle Perimeter Formula

P = 2L + 2 W

Let

48 = Length

24 = Width

144 = Perimeter

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144 = 2 (48) + 2(24)

144 =96 + 48

144 = 144

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The largest Possible area

The length is 48

The width is 24

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Answer 3

usualy the biggest area that a triangle can ocupie is when all the sides are equal 60 degree angle. (there is a proof for that)

sop if L=144 then a=144/3=48

and P=[48^2 * sqrt(3) ] /4

sqrt(3) square root from 3 (a formula for even side triangle)

and P=997


The upper answer is not good because it uses just 3 sides for a perimeter and a formula for a rectangle area

Answer 4

I assume you're measuring in feet.
If you make a square pen & count the barn wall as a side:
144/4 = 36 ft. each side
36 x 36 = 1,296 sq. ft.
If you make it rectangular, it comes out the same.