Saturday

April 18, 2015

April 18, 2015

Posted by **Jen** on Saturday, November 18, 2006 at 11:01pm.

A 216m^2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. What dimensions for the outer rectangle will require the smallest total length of fence? How much fence will be needed.

Thank you all for helping.

Let's suppose your dividing fence is vertical and has a length of x. Let the length of the other side be y.

Since the area must be 216, y = 216/x

Perimeter P = 3x + 2y which after substituting is equal to 3x + 432/x

Find derivative: dP/dx = 3 - 432/x^2. Set it to zero and solve for x.

3x^2 = 432

x^2 = 144

We can accept the positive solution only. Therefore, x = 12.

y = 18 (sub 12 for x into y = 216/x)

The dimensions are 18m and 12m

**Answer this Question**

**Related Questions**

Math - A rectangular study area is to be enclosed by a fence and divided into ...

math - i am having serious optimization problems. i don't get it!!! plz help. a ...

calculus (optimization) - a rectangular study area is to be enclosed by a fence ...

area and perimeter - a farmer wishes to build a fence around a rectangular field...

Grade 11 Math - A rectangular dog run is to be enclosed by a fence and then ...

Calculus 1 - A rectangular field is enclosed by a fence and seperated into two ...

calculus - A 384 square meter plot of land is to be enclosed by a fence and ...

calculas - A landowner wants to fence in a rectangular area of 60000 square ...

MATH - A landowner wants to fence in a rectangular area of 75000 square metres ...

precalculus - A rectangular field is to be enclosed by a fence and divided into...