Question

Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find the maximum length of a side of the garden.

Short answer

The maximum length of a side of garden is 15 feet.

Step-by-step solution

Step 1. State the concept of fencing.

Fencing a garden means building fences around that garden. This fencing length is equal to the perimeter of that garden. Here, the shape of the garden is in square. The perimeter of square is 4 times the length of the side of the square.

Step 2. Construct the inequation.

The square has 4 equal sides.

The perimeter of the square is 4 times side.

Let the side represent xfeet.

As he has 60 feet of fencing, this means the perimeter of the garden must be less than or equal to 60.

$4x\le 60$

Step 3. Solve the inequation.

Solve for x, the maximum length of the side..

$\begin{array}{c}4x\le 60\\ \frac{4x}{4}\le \frac{60}{4}\\ x\le 15\end{array}$

So, the maximum length of the side of the garden is 15 feet.

Thus, themaximum length of a side of garden is 15 feet.