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.

About how long should the diagonal piece of wood be?

Answer 1

To find the length of the diagonal piece of wood, we can use the Pythagorean theorem. In this case, the other two sides are the vertical boards. Therefore, the diagonal piece of wood should be approximately 113.25 inches long.

Step-by-step explanation:

To find the length of the diagonal piece of wood, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. In this case, the other two sides are the vertical boards. Since each vertical board is 8 inches wide, and there are 12 vertical boards, the total width of the vertical boards is 8 inches x 12 = 96 inches.

So, we have a right triangle with one side measuring 96 inches and the other side measuring 5 feet (or 5 feet x 12 inches/foot = 60 inches). Let's use 'a' to represent the length of the diagonal piece (hypotenuse).

Using the Pythagorean theorem, we can write the equation:

a^2 = 96^2 + 60^2

a^2 = 9216 + 3600

a^2 = 12816

a = sqrt(12816)

a ≈ 113.25 inches

Therefore, the diagonal piece of wood should be approximately 113.25 inches long.