Copyright 2011 Study Island - All rights reserved. Pythagorean Theorem

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1 Generation Date: 04/11/2011 Copyright 2011 Study Island - All rights reserved. Generated By: KATHLEEN MC LEAD Pythagorean Theorem 1. Two ships leave port at the same time. Ship X is heading due north and Ship Y is heading due east. Twelve hours later they are 600 miles apart. If the Ship X had traveled 480 miles from the port, how many miles had Ship Y traveled? A. 120 miles B. 300 miles C. 360 miles D. 420 miles 2. 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? A. 16 ft B ft C. 21 ft D. 15 ft 3. Two cars leave a dealership at the same time. Car J is heading south on Interstate 45, and Car K is heading west on Interstate 20. Two hours later they are 115 miles apart. If Car J had traveled 92 miles from the dealership, how many miles had Car K traveled? A. 69 B. 92 C. 138 D In the tent pictured below, the vertical post, x, is perpendicular to the ground. The post is 49 inches in length. The distance from the post to the edge of the

2 tent, y, is 43 inches. Approximately, what is the tent's slant height, z? picture not drawn to scale A. 69 inches B. 72 inches C. 65 inches D. 92 inches 5. If M = 35 cm and N = 37 cm, what is the length of L? A. B. C. D. 6. Firefighters have a 39-foot extension ladder. In order to reach 36 feet up a building, how far away from the building should the foot of the ladder be placed?

3 A. 15 feet B. 3 feet C. 18 feet D. 21 feet 7. Peter accidentally threw his frisbee on top of his school, 12 feet above the ground. Since he works part-time at the local hardware store, he went down to the store to borrow a ladder. There is a row of bushes along the edge of the school, so he will have to place the ladder 9 feet from the building. What is the minimum length of ladder that he needs to reach the top of the school? A. 21 feet B. 18 feet C. 15 feet D. 9 feet 8. Jason accidentally locked himself out of his apartment, but remembered that he left a window open. The window is 12 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 9 feet from the building. What length of ladder will Jason need to reach the window? A. 15 feet B. 9 feet C. 12 feet D. 18 feet 9. Kenny's parents are letting him and some friends build a skate ramp. The boys have decided they would like the ramp to be 3 feet long and 1.5 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? A. 3.4 feet B. 2.3 feet C. 4.5 feet D. 2.6 feet

4 10. If N = 37 cm and L = 12 cm, what is the length of M? A. B. C. D. Answers 1. C 2. D 3. A 4. C 5. D 6. A 7. C 8. A 9. D 10. C Explanations

5 1. Let x represent the distance traveled by Ship X, y represent the distance traveled by Ship Y, and z represent the distance between the two ships. Now, use the Pythagorean theorem. So, Ship Y traveled 360 miles east y 2 = ,400 + y 2 = 360,000 y 2 = 360, ,400 y 2 = 129,600 y = If the room is a perfect rectangle, then each diagonal will cut the room into two congruent right triangles. The red diagonal cuts the room into right triangles R1 and R2 and the blue diagonal cuts the room into right triangles B1 and B2. Since the length and width are the same for either set of right triangles, the length of the diagonals can be found using the Pythagorean theorem. width 2 + length 2 = diagonal 2 (9 ft) 2 + (12 ft) 2 = diagonal 2 81 ft ft 2 = diagonal ft 2 = diagonal 2 15 ft = diagonal So, each diagonal should be exactly 15 ft long. 3. Let x represent the distance traveled by Car J, y represent the distance traveled by Car K, and z represent the distance between the two cars. Now, use the Pythagorean theorem. (92 miles) 2 + y 2 = (115 miles) 2 8,464 miles 2 + y 2 = 13,225 miles 2 y 2 = 13,225 miles 2-8,464 miles 2 y 2 = 4,761 miles 2 y = 69 miles So, Car K traveled 69 miles west. 4. Given that the post is perpendicular to the ground, the Pythagorean theorem can be used to solve for z.

6 (49 in) 2 + (43 in) 2 = z 2 2,401 in 2 + 1,849 in 2 = z 2 4,250 in 2 = z 2 65 in z Therefore, the slant height of the tent is approximately 65 inches. 5. Use the Pythagorean theorem. 6. Let x represent how far away the foot of the ladder should be from the building, y represent how far up the building the ladder needs to reach, and z represent the length of the ladder. Now, use the Pythagorean theorem: x 2 + (36 ft) 2 = (39 ft) 2 x 2 + 1,296 ft 2 = 1,521 ft 2 x 2 = 1,521 ft 2-1,296 ft 2 x 2 = 225 ft 2 x = 15 ft So, the foot of the ladder needs to be placed 15 feet away from the building. 7. Let x represent the height of the school, y represent the how far the base of the ladder is from the school, and z represent the length of the ladder. Now, use the Pythagorean theorem. (12 ft) 2 + (9 ft) 2 = z ft ft 2 = z ft 2 = z 2 15 ft = z So, the ladder must be at least 15 feet long. 8. Let x represent the height of the window, y represent the how far Jason needs to be away from the building, and z represent the length of the ladder. Now, use the Pythagorean theorem: (12 ft) 2 + (9 ft) 2 = z 2

7 144 ft ft 2 = z ft 2 = z 2 15 ft = z So, the ladder must be at least 15 feet long. 9. Let x represent the height of the ramp, y represent the length of the base of the ramp, and z represent the length of the ramp. Now, use the Pythagorean theorem. (1.5 ft) 2 + y 2 = (3 ft) ft 2 + y 2 = 9 ft 2 y 2 = 6.75 ft 2 y 2.6 ft Therefore, the base of the skate ramp will be approximately 2.6 feet. 10. Use the Pythagorean theorem. Copyright 2011 Study Island - All rights reserved.