Pythagorean Theorem 1. To make room for the new baby, Glenn is adding a room to his house. The blueprints for the addition indicate that the room should be a rectangle with dimensions of 9 ft wide by 12 ft long. Glenn just finished the framing and wants to make sure the room is a perfect rectangle before he starts putting up the drywall. To do this he measures the diagonals of the room, which should be the same length. How long should each diagonal be? 2. Two ships leave port at the same time. Ship X is heading due north and Ship Y is heading due east. Eight hours later they are 400 miles apart. If the Ship X had traveled 320 miles from the port, how many miles had Ship Y traveled? 3. If Z = 15 cm and X = 17 cm, what is the length of Y? 4. Jason accidentally locked himself out of his apartment, but remembered that he left a window open. The window is 16 feet above the ground. Since he works part-time at the local hardware store, he went to the store to borrow a ladder. There's a row of bushes along the edge of the apartment, so he will have to place the ladder 12 feet from the building. What length of ladder will Jason need to reach the window?
5. If M = 35 cm and N = 37 cm, what is the length of L? 6. If X = 17 cm and Y = 8 cm, what is the length of Z? 7. A fire truck parks 20 feet away from a building. The fire truck extends its ladder 52 feet. How far up the building from the truck's roof does the extension ladder reach?
8. Chad and his friends like to play in a grass field that sits between 1st Street, Cowboy Avenue, and Aikman Drive as shown below. If the distance from the intersection of 1st Street and Aikman Drive to the intersection of 1st Street and Cowboy Avenue is 60 yards and the distance from the intersection of 1st Street and Cowboy Avenue to the intersection of Cowboy Avenue and Aikman Drive is 25 yards, what is the distance from the intersection of 1st Street and Aikman Drive to the intersection of Cowboy Avenue and Aikman Drive? 9. Two ships leave port at the same time, Ship X is heading due north and Ship Y is heading due east. Fourteen hours later they are 700 miles apart. If the Ship X had travels 560 miles from the port, how many miles will Ship Y travel?
10. In the roof design below, the lower support beam, A, is 21 feet. The vertical support beam, B, is 16 feet. The two beams meet at a right angle. What is the minimum length necessary for the angled support beam, C? picture not drawn to scale 11. If S = 7 cm and T = 24 cm, what is the length of R?
12. Tri-Star Industries employs electrical, plumbing, and air conditioning technicians. Their home office is made up of three square buildings, one for each department, with a triangular atrium in the middle. If the area of the Plumbing building is 3,600 ft 2 and the area of the A/C building is 625 ft 2, what is the area of the Electrical building? 13. *Note: Picture not drawn to scale. 14. If L = 12 cm and M = 35 cm, what is the length of N?
15. Steve is rebuilding his mailbox post. The horizontal portion is 18 inches, where a is 13 inches. The vertical post is 45 inches, where b is 12 inches. Those two pieces meet at a right angle. What is the minimum length necessary for the angled support, c? picture not drawn to scale 16. Kenny's parents are letting him and some friends build a skate ramp. The boys have decided they would like the ramp to be 6 feet long and 3 feet high. The base of the ramp, y, meets the back of the ramp, x, at a right angle. Approximately how long is the base of the ramp?
17. *Note: Picture not drawn to scale. 18. A Blipco television has a rectangular screen with a diagonal measurement of 20 inches. If the screen has a height of 12 inches, what is the width of the screen?
19. Carson found an old tent in the attic of his house and decided to set it up in the back yard. However, the support sticks for the tent are missing. If the tent is 72 inches across on the bottom and 45 inches on each side, how tall of a stick does he need to set up the tent? 20. *Note: Picture not drawn to scale.