Question

1. you are building a fence around your vegetable garden in your backyard. if the garden is 128\ long and 46\ wide, what is the total length of fencing you will need? draw a diagram. state your answer in feet and inches.

Explanation:

Step1: Convert dimensions to inches

First, convert the length and width from feet and inches to just inches.

• Length: \( 12 \) feet \( 8 \) inches. Since \( 1 \) foot \( = 12 \) inches, \( 12 \) feet \( = 12\times12 = 144 \) inches. So total length in inches is \( 144 + 8 = 152 \) inches.
• Width: \( 4 \) feet \( 6 \) inches. \( 4 \) feet \( = 4\times12 = 48 \) inches. So total width in inches is \( 48 + 6 = 54 \) inches.

Step2: Calculate perimeter in inches

The garden is a rectangle, and the perimeter \( P \) of a rectangle is given by \( P = 2\times (length + width) \).
Substitute the length and width in inches: \( P = 2\times(152 + 54) = 2\times206 = 412 \) inches.

Step3: Convert perimeter back to feet and inches

Now, convert \( 412 \) inches back to feet and inches. Divide \( 412 \) by \( 12 \): \( 412\div12 = 34 \) with a remainder of \( 4 \) (because \( 34\times12 = 408 \), and \( 412 - 408 = 4 \)). So, \( 412 \) inches is \( 34 \) feet \( 4 \) inches.

Alternatively, we can calculate the perimeter by first finding the sum of length and width in feet and inches, then doubling it.

• Length: \( 12'8'' \), Width: \( 4'6'' \)
• Sum of length and width: \( 12'8'' + 4'6'' = (12 + 4)' + (8 + 6)'' = 16'14'' \). Since \( 14'' = 1'2'' \), this becomes \( 17'2'' \).
• Perimeter: \( 2\times(17'2'') = 34'4'' \).

Answer:

The total length of fencing needed is \( 34 \) feet \( 4 \) inches.