A carpenter added a diagonal brace to a gate that measures 45 inches wide and 55 inches tall. How long is the brace to the nearest tenth of an inch?

71.1 inches

Step-by-step explanation:

The problem can be represented by rectangle with a diagonal, as shown in the diagram below.

The diagonal brace splits the rectangular gate into two equal right angled triangles, hence, we can solve this problem by applying Pythagoras theorem.

It states that:

hyp² = opp² + adj²

Where opp is the opposite side and adj is the adjacent side to the angle of consideration (which is not necessary in this question)

The diagonal brace is the hypotenuse of the triangle, x.

Hence:

x² = 45² + 55²

x² = 2025 +3025

x² = 5050

Finding the square root,

x = 71.1 inches (approximated to the nearest tenth of an inch)

The diagonal brace is 71.1 inches long.