Pythagorean Theorem Applications

The owners of a house want to convert a stairway leading from the ground to their back
porch into a ramp. The porch is 3 feet off the ground, and due to building regulations, the ramp
must start 12 feet away from the base of the porch. How long will the ramp be?

​​Example 1

Xavier walked 8 blocks due East and then 7 blocks due South. What is the shortest distance, in blocks, from the point where Xavier started to where he ended?

Example 2

You’re locked out of your house and the only open window is on the second floor, 30 feet above the ground. You need to borrow a ladder from one of your neighbors. There’s a flower garden along the edge of the house, so you’ll have to place the ladder 12 feet from the house. What length of ladder do you need to reach the window?

​​Example 3

Mary is trying to keep frogs from her garden. If her rectangle garden has a length of 15 inches and a width of 9 inches. What is the diagonal in inches of the garden?

Example 4

What is the height of the isosceles triangle with side lengths of 9 and a base of 14?

​​Example 5

Dylan wants to get from point A to point C as quickly as possible. He can climb the stairs directly from A to C at a rate of 10 meters per minute, or he can bike along the bike path from A to B to C at the rate of 30 meters per minute. If AB is perpendicular to BC, AB = 90 meters, and BC = 120 meters, which route will get Dylan to point C in less time?

​​Example 6