Pythagoras Word Problems

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?

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

• Divide both sides by 2

• Take the square root of both sides

How far from the base of a house do you need to place a 15' ladder so that is exactly reaches the top of a 12' wall?

• 9 feet

• 19.2 feet

• 81 feet

• 369 feet

To get from one side of the pond to the other you must walk 34 meters south and 41 meters east.  To the nearest meter, how many less meters would it take if it were possible to go directly across the pond.  

• 53

• 22

• 75

• 9

Johnathan is painting the side of his home. He has a 25 foot ladder and leans the ladder against his house. The base of the ladder is five feet from the side of the house. How far up the house will the ladder reach?

• 24.5 ft

• 25.5 ft

• 26.5 ft

• 23.5 ft