Pythagorean Theorem Word Problems

The bottom of a 13-foot ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach? Which equation could be used to solve the problem?

How far from the base of a house do you need to place a 15 foot ladder so that is exactly reaches the top of a 12 foot wall? Which equation could be used to solve the problem?

• 12 + b = 15

The diagonal of a rectangle is 25 inches. The width is 15 inches. Which equation could be used to solve the problem?

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point? Which equation could be used to solve the problem?

If the two legs of a right triangle measure 8 inches and 12 inches, what is the length of the hypotenuse? Which equation could be used to solve the problem?

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be? Which equation could be used to solve the problem?

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other? Which equation could be used to solve the problem?

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew? Which equation could be used to solve the problem?

John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school? Which equation could be used to solve the problem?

The hypotenuse of a right triangle is 12 feet and one of its legs is 3 feet. What is the length of the other leg? Which equation could be used to solve the problem?