Question

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

Answer 1

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).