Question

A carpenter wants to build a diagonal brace for a rectangular gate that is 5 feet wide and 7 feet high. Approximately what is the length, in feet, of the diagonal brace?

1) 5.5
2) 6.5
3) 7.5
4) 8.5
5) 9.5

Answer 1

To find the length of the diagonal brace for a rectangular gate, we can use the Pythagorean theorem. By applying the theorem with the width and height of the gate, we can approximate the length of the diagonal brace to be 8.6 feet.

Step-by-step explanation:

To find the length of the diagonal brace, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the width of the gate is one side of the right triangle, the height of the gate is the other side, and the diagonal brace is the hypotenuse. So, we have:

Width of gate = 5 feet

Height of gate = 7 feet

Let's call the length of the diagonal brace 'x'. According to the Pythagorean theorem:

x^2 = (5^2) + (7^2)

x^2 = 25 + 49

x^2 = 74

Now, we need to find the square root of 74 to get the length of the diagonal brace:

x = √74

Simplifying this, we get:

x ≈ 8.6 feet

So, approximately, the length of the diagonal brace is 8.6 feet.