Sahar S. answered • 04/14/15

Math/General Chem/Physics Tutor

(For writing purposes I am going to call the Length of the fence L and the Width of the fence W)

First, Lets break down what this word problem gives us.

We know that the fence is a rectangle

and the Length of the fence is 12 more than the Width

when you see the phrase "more than" you should think addition. We can set this up as L = 12 + W

Next, we see that Farmer Dan has a total of 100 feet of fencing to work with

What is the equation we should use to find the Perimeter (P) of a rectangle?

P = L + L + W + W --> P = 2L +2W

and we know that the Length is 12 more than the Width (L = 12 + W) so let's substitute this into our Perimeter equation

P = 2 ( 12 + W ) + 2W

now we have to set this up in an inequality to get the largest perimeter

2(12+W) + 2W ≤ 100

( Note: we use the "less than or equal to" inequality because we know that we cannot have more than 100 feet of fencing because that is all Farmer Dan has on him so we can either try to use all of the fencing material he has or less than what he has. )

Simplifying this inequality we get

24 + 2W + 2W ≤ 100

24 + 4W ≤ 100

4W ≤ 100 - 24

4W ≤ 76

W ≤ (76/4)

W ≤ 19

if we say the Width,

**W = 19**What should our Length be? L = 12 + W

L = 12 + 19

**L = 31**

What is the perimeter?

P = 2L + 2W

P = 2 (31) + 2 (19)

P = 62 + 38

P = 100 feet

the largest fence farmer Dan can build with the rule given ( length of a rectangular fenced enclosure is 12 feet more than the width) is 100 feet perimeter

the dimensions of the fence would be the Length = 31 feet and the Width = 19 feet

the Area (A) of this fence is found by multiplying the Length and the Width together

A = L*W

A = 31 * 19 = 589 square-feet