Pythagorean Word Problems

Pythagorean Word Problems Answer each question on your piece of paper. In order to receive full credit you must: Draw a picture. Show how you plugged the numbers into the Theorem. Write your final answer in a complete sentence.

Question #1 • To wash a window that is 12 feet off the ground, Lazaro leans a 20-foot ladder against the side of the building. To reach the window, how far away from the building should Lazaro place the base of the ladder?

Question #2 • Noelia takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is 3 inches long and 4 inches wide, how long is the diagonal cut that Noelia made?

Question #3 • An envelope is 15 centimeters wide, and it measures 17 centimeters along the diagonal. How tall is the envelope?

Question #4 • Tessa takes a rectangular piece of fabric and cuts from one corner to the opposite corner. If the piece of fabric is 12 centimeters long and 16 centimeters wide, how long is the diagonal cut that Tessa made?

Question #5 • To wash a window that is 8 meters off the ground, Amanda leans a 10-meter ladder against the side of the building. To reach the window, how far away from the building should Amanda place the base of the ladder?

Question #6 • Mrs. Tate is teaching a 5th grade class. She is standing 12 feet in front of Fusa. Melissa is sitting 9 feet to Fusa's right. How far apart are Mrs. Tate and Melissa?

Question #7 • Aaron would have to drive due north to get to his parents' house and due east to get to his grandparents' house. It is 12 kilometers from Aaron's house to his parents' house and a straight-line distance of 13 kilometers from his parents' house to his grandparents' house. How far is Aaron from his grandparents' house?

Question #8 • Stafford is 8 miles due north of the airport, and Hudson is 15 miles due east of the airport. How far apart are Stafford and Hudson?

Question #9 • Whenever he visits Auburn, Trent has to drive 56 kilometers due north from home. Whenever he visits Yardley, he has to drive 42 kilometers due east from home. How far apart are Auburn and Yardley, measured in a straight line?

Question #10 • On the school playground, the slide is due west of the tire swing and due south of the monkey bars. If the distance between the slide and the tire swing is 12 meters and the distance between the tire swing and the monkey bars is 15 meters, how far is the slide from the monkey bars?

Question #11 • A farmer is tilling a rectangular field that is 60 meters long and 63 meters wide. What is the distance between opposite corners of the farmer's field?

Question #12 • Nicole takes a piece of plywood that is 12 inches long and uses a table saw to make a 20-inch cut from corner to opposite corner. What was the width of the piece of plywood?

Question #13 • Reggie is in a hot air balloon that has just taken off and is now floating 8 meters above its launching point. Yong Sook is standing on the ground, 6 meters away from the launching point. How far apart are Reggie and Yong Sook?

Question #14 • Three ballet dancers are positioned on stage. If Ronald is 4 feet straight behind Todd and 3 feet directly left of Dominic, how far is Todd from Dominic?

Question #15 • Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 16 miles. If the two airplanes are 20 miles apart, how far has the eastbound airplane traveled?

Question #16 • Amalia is fishing from a small boat. Her fishing hook is 15 meters below her, and a fish is swimming at the same depth as the hook, 8 meters away. How far away is Amalia from the fish?

Question #17 • To repair a roof that is 4 meters high, Mr. Ellis leans a 5-meter ladder against the side of the building. To reach the roof, how far away from the building should he place the base of the ladder?

Question #18 • Candice is building a slide for her kids. If the ladder is 5 feet tall and she wants the bottom of the slide to be 12 feet from the ladder, how long does the slide need to be?

Question #19 • Three baseball players are playing catch. LaVonne is 6 meters south of Gina and 8 meters west of Alicia. How far does Gina need to throw the ball to get it to Alicia?

Question #20 • A flying squirrel's nest is 12 feet high in a tree. From its nest, the flying squirrel glides 15 feet to reach an acorn that is on the ground. How far is the acorn from the base of the tree?

Question #21 • Donna's TV screen is 20 inches long. If the diagonal measures 25 inches, how long is the width of Donna's TV?

Question #22 • If the legs of an isosceles right triangle are 5 inches long, approximate the length of the hypotenuse to the nearest whole number.

Question #23 • Scott wants to swim across a river that is 400 meters wide. He begins swimming perpendicular to the shore he started from but ends up 100 meters down river from where he started because of the current. How far did he actually swim from his starting point?

Question #24 • In construction, floor space must be given for staircases. If the second floor is 3.6 meters above the first floor and a contractor is using the standard step pattern of 28 cm of tread for 18 cm of rise then how many steps are needed to get from the first to the second floor and how much linear distance will need to be used for the staircase?

Question #25 • The area of a square is 81 square centimeters. Find the length of a side. Find the length of the diagonal.

Question #26 • An isosceles triangle has congruent sides of 20 cm. The base is 10 cm. Find the height of the triangle.

Question #27 • Jill’s front door is 42” wide and 84” tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door? Explain using approximations.

Question #28 • Kathy Holt is getting married and her parents are planning a garden wedding. They rented a large tent for the backyard and Mr. Holt wants to anchor the tent poles. The poles are each 10 feet high and he plans to run a wire from the top of the pole to a stake in the ground 4 feet from the base of the pole. How long is the wire?

Question #29 • As part of a community service project, the Key Club wants to build a ramp to make the stage in the auditorium wheelchair accessible. The stage is 4 feet above ground level and they want the ramp to start its slope 8 feet from the base of the stage. To insure that the ride is smooth, they want to buy boards that are long enough to cover the entire distance from where the slope begins to the top of the stage. At the lumberyard, they discover that boards come in lengths of 8 feet, 10 feet, 12 feet and 14 feet. What length boards should they buy?

Question #30 • A fireman’s ladder is 80 feet long and must be positioned so that the foot of the ladder is no closer than 30 feet from the base of the building. There is a fire in a 6 story building and each floor is 10 feet above the one below it. Will the ladder be adequate to reach the top floor of the building?

Question #31 • Two boats leave the same dock at the same time. One travels north at 6 mph and the other travels east at 8 mph. How far apart will the boats be after 4 hours?

Question #32 • Kelly just bought a high definition TV that has a 36 inch diagonal screen. The TV is 2 feet tall. Will the TV fit in a cabinet that is 27 and ½ inches wide?

Question #33 • A football field is 100 yards with 10 yards at each end for the end zones. The field is 45 yards wide. Find the length of the diagonal of the entire field, including the end zones.

Pythagorean Word Problems