I think its D, I found the key to ur test or smth else online, if the first questions is which statement about triangle is true the. It’s Also the longest answer out of all of them

7 0

3 years ago

ol McDonald would like to build a pin for his favorite pig horse and cow he needs to enclose a rectangular plot of land into thr

garri49 [273]

The area of the pen is the products of its dimensions

The dimension of the pen is 300 by 120 feet
The maximum area of the pen is 36000 square feet.

Let the dimension of the fence be x by y.

So, we have:

$\mathbf{2x + 5y = 1200}$ --- perimeter

$\mathbf{Area =xy}$ -- area

Subtract 5y from both sides of $\mathbf{2x + 5y = 1200}$

$\mathbf{2x = 1200 - 5y}$

Divide both sides by 2

$\mathbf{x = \frac{1200 - 5y}{2}}$

Substitute $\mathbf{x = \frac{1200 - 5y}{2}}$ in $\mathbf{Area =xy}$

$\mathbf{Area = \frac{1200 - 5y}{2} \times y}$

$\mathbf{Area = \frac{1200y - 5y^2}{2}}$

Split

$\mathbf{Area = 600y - \frac{5}{2}y^2}$

Differentiate

$\mathbf{A' = 600 -5y}$

Set to 0

$\mathbf{600 -5y = 0}$

Add 5y to both sides

$\mathbf{5y = 600}$

Divide both sides by 5

$\mathbf{y = 120}$

Substitute $\mathbf{y = 120}$ in $\mathbf{x = \frac{1200 - 5y}{2}}$

$\mathbf{x = \frac{1200 - 5 \times 120}{2}}$

$\mathbf{x = \frac{1200 - 600}{2}}$

$\mathbf{x = \frac{600}{2}}$

$\mathbf{x = 300}$

Recall that:

$\mathbf{Area =xy}$

So, we have:

$\mathbf{Area = 300 \times 120}$

$\mathbf{Area = 36000}$

Hence, the maximum area of the pen is 36000 square feet.