Matt is repairing a gate and needs to nail a brace diagonally to strengthen the posts. If the hieght of the post is 48 inches and there is 6

Question

Matt is repairing a gate and needs to nail a brace diagonally to strengthen the posts. If the hieght of the post is 48 inches and there is 64 inches between posts, in inches, what should the length of the diagonal brace be on order to fit between the posts?
(a) 80 inches
(b) 42 inches
(c) 15 inches
(4) inches

0

1. We have to realize that the height of a post and the horizontal distance between the posts form a right angle. Then the diagonal that joins the highest point of a post and the lowest point of the other post is the hypotenuse of a right triangle. Then we can apply the Pythagorean theorem to calculate the length of this hypotenuse.​

According to the Pythagorean theorem H² = P² + D² where H is the hypotenuse (diagonal) and P the height of a post (cathetus) and D the distance between posts (cathetus).​

Since we know these values, we can replace them :​

H² = (48inches)² + (64inches)² = 2,304inches² + 4,096inches² = 6,400inches²​

H = = 80inches​