Question

George is building a rectangular gate. He fastens a brace diagonally at the corners to keep the gate sturdy. If the brace is 7 feet long and the gate is 5 feet tall, how wide is the gate? a) 7 feet b) 9 feet c) 12 feet d) 10 feet

Answer 1

George's rectangular gate can be considered as a right triangle with the diagonal brace as the hypotenuse. By applying Pythagoras' theorem, we find that the width should be approximately 4.9 feet.

Step-by-step explanation:

In this problem, George is building a rectangular gate and he fastens a brace (diagonal) from one corner to the other to keep it sturdy. This setup forms a right triangle whose sides are the height, width, and diagonal of the gate. If we know the height (5 feet) and the diagonal (7 feet), we can use Pythagoras' Theorem (a^2 + b^2 = c^2) to find the width (b). The equation becomes: (5^2) + b^2 = (7^2).

1. Subtract 25 from both sides of the equation: b^2 = 49-25.
2. Simplify the right side: b^2 = 24.
3. Take the square root of both sides: b = sqrt(24).

The width of the gate, b, is √24 which roughly equals 4.9 feet. Unfortunately, this answer is not in the given choices, but this is how you would use Pythagoras' theorem to solve the problem.

Learn more about Pythagoras' Theorem