Question

a farmer wants to build a fence in the shape of a parallelogram for his animals. The perimeter of the fence will be 600 feet, and the North/South fences are half of the length of the West/East fences. If fences are sold in 5 foot segments, how many fence segments does the farmer need to buy ?

Answer 1

Let's use the variable L to represent the length and W to represent the width.

If the perimeter is 600 ft, we have:

$\begin{gathered} P=2L+2W\\ \\ 2L+2W=600\\ \\ L+W=300 \end{gathered}$

The width is half the length, so we have:

$\begin{gathered} W=\frac{L}{2}\rightarrow L=2W\\ \\ 2W+W=300\\ \\ 3W=300\\ \\ W=\frac{300}{3}\\ \\ W=100\text{ ft}\\ \\ L=200\text{ ft} \end{gathered}$

Now, if each fence segment is 5 ft, we number of segments needed is:

$\begin{gathered} \text{ fences for W1: }\frac{100}{5}=20\\ \\ \text{ fences for W2: }\frac{100}{5}=20\\ \\ \text{ fences for L1:}\frac{200}{5}=40\\ \\ \text{ fences for L2:}\frac{200}{5}=40\\ \\ \\ \\ \text{ total:}20+20+40+40=120\text{ fence segments} \end{gathered}$