Question

Wally is rebuilding his fence. Each section of the fence will have 12 vertical boards that are each eight inches wide. He’s going to attach them to two horizontal pieces of wood and add a diagonal piece to brace the fence section. The horizontal pieces will be five feet apart.

1.About how long should the diagonal piece of wood be?

2. If Wally plans on using 30 sections of fence, about how many feet of wood will he need for the horizontal and diagonal pieces?

Answer 1

Part A)

Each diagonal is about 9.43 feet.

Part B)

In total, Wally needs about 736.02 feet of wood.

Explanation:

Part A)

Since each vertical board has a width of 8 inches, for one section with 12 vertical boards, the total width will be 8(12) = 96 inches.

96 inches is the same as 96/12 = 8 feet.

We are also given that the horizontal pieces will be 5 feet apart.

To find the diagonal, we can use the Pythagorean Theorem. The 8 is the base and 5 is the height. Therefore:

`\displaystyle d^2=8^2+5^2`

Compute:

`d^2=89`

Taking the square root, we acquire:

`\displaystyle d=√(89)\approx9.43 \text{ feet}`

So, each diagonal is about 9.43 feet.

Part B)

For each section, we have two horizontal pieces (each 8 feet) and one diagonal piece (each √89 feet).

Therefore, for one section, we will need a total of:

`\displaystyle L=8+8+√(89)=16+√(89)`

Then for 30 sections, we will need:

`T=30(16+√(89))`

Approximate:

`T\approx 763. 02`

Wally will need about 736.02 feet of wood in total.