Answer:
71.1 inches
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.