A carpenter added a diagonal brace to a gate. The gate is 80 inches wide and 60 inches tall. How long is the brace?

We can use the Pythagorean theorem to solve for the diagonal (hypotenuse) length of the gate. This theorem states that a^2 + b^2 = c^2 where a and b are the leg lengths and c is the hypotenuse length. In this case, 80^2 + 60^2 = 6400 + 3600 = 10,000 = c^2. Taking the square root, we see that the length of the brace is 100 inches (thus making the gate a standard 3-4-5 right triangle).