A homeowner wants to use part of her yard for a garden. She decides that the garden is to be 9 ft longer than its​ width, w. If she wants to put a fence around the​ garden, how much fencing does she need to​ buy?

Question

She needs to buy( )ft of fencing.

Answer 1

To determine how much fencing the homeowner needs to buy, we first need to establish the dimensions of the garden.

Let the width of the garden be \( w \) feet. According to the problem, the length of the garden is \( w + 9 \) feet.

Now we can calculate the perimeter of the rectangle (the garden) using the formula for the perimeter \( P \) of a rectangle:

\[ P = 2 \times (\text{length} + \text{width}) \]

Substituting the expressions for length and width into the formula:

\[ P = 2 \times ((w + 9) + w) \]

This simplifies to:

\[ P = 2 \times (2w + 9) \]

Now, distributing the 2 gives:

\[ P = 4w + 18 \]

Therefore, the total amount of fencing needed is \( 4w + 18 \) feet.

To provide a specific numerical answer, we would need to know the value of \( w \) (the width). However, if the homeowner simply wants a formula based on the width she chooses, then she needs to buy \( 4w + 18 \) feet of fencing.