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Leto [7]
3 years ago
15

A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fen

cing. What is the largest area that can be enclosed?
Mathematics
1 answer:
baherus [9]3 years ago
3 0

Answer:

Area = 2500 square feet is the largest area enclosed

Step-by-step explanation:

A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing

Let x be the length of each box and y be the width of the box

Perimeter of the box= 3(length ) + 4(width)

200=3x+4y

solve for y

200=3x+4y

200-3x=4y

divide both sides by 4

y=50-\frac{3x}{4}

Area of the rectangle = length times width

Area = 3x \cdot y

Area = 3x \cdot (50-\frac{3x}{4})

A=150x-\frac{9x^2}{4}

Now take derivative

A'=150-\frac{9x}{2}

Set it =0 and solve for x

0=150-\frac{9x}{2}

150=\frac{9x}{2}

multiply both sides by 2/9

x=\frac{100}{3}

A''=-\frac{9}{2}

For any value of x, second derivative is negative

So maximum at x= 100/3

 A=150x-\frac{9x^2}{4} , replace the value of x

A=150(\frac{100}{3})-\frac{9(\frac{100}{3})^2}{4})

Area = 2500 square feet is the largest area enclosed

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