Practice with Pythagorean Theorem Topic Index | Algebra Index | Regents Exam Prep Center
 Answer the following questions dealing with the Pythagorean Theorem.
 1. To get from point A to point B you must avoid walking through a pond.  To avoid the pond, you must walk 34 meters south and 41 meters east.  To the nearest meter, how many meters would be saved if it were possible to walk through the pond? Choose: 22 34 53 75 Explanation Walking around covers a distance of 75 m. Use Pythagorean theorem to find the hypotenuse. The hypotenuse = 53.3 m. Walking through the pond saves 22 m.

 2. A baseball diamond is a square with sides of 90 feet.  What is the shortest distance, to the nearest tenth of a foot, between first base and third base? Choose: 90.0 127.3 180.0 180.7 Explanation Use the Pythagorean Theorem. a and b both equal 90. Solving for c gives c = 127.3.

 3. A suitcase measures 24 inches long and 18 inches high.  What is the diagonal length of the suitcase to the nearest tenth of a foot? Choose: 2.5 2.9 26.5 30.0 Explanation Use Pythagorean Theorem to find the diagonal. Let a = 24 and b = 18. When solved, c = 30 inches. Convert inches to feet by dividing by 12. 30 / 12 = 2.5 feet.

 4. In a computer catalog, a computer monitor is listed as being 19 inches.  This distance is the diagonal distance across the screen.  If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch? Choose: 10 14 16 19 Explanation Use the Pythagorean Theorem c=19 and a=10 When solved, b=16.2

 5. The older floppy diskettes measured 5 and 1/4 inches on each side.  What was the diagonal length of the diskette to the nearest tenth of an inch? Choose: 5.3 6.5 7.4 7.6 Explanation Use the Pythagorean Theorem a and b both equal 5.25 When solved, c=7.4

 6. Ms. Green tells you that a right triangle has a hypotenuse of 13 and a leg of 5.  She asks you to find the other leg of the triangle without using paper and pencil.  What is your answer? Choose: 5 8 10 12 Explanation Use the Pythagorean Triple 5, 12, 13. The other leg must be 12.

 7. Two joggers run 8 miles north and then 5 miles west.  What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point? Choose: 8.4 9.5 9.4 13.1 Explanation Use the Pythagorean Theorem a=8 and b=5 When solved, c=9.439

 8. Find x Choose: 6 8 10 12 Explanation Use the Pythagorean Theorem or use the Pythagorean Triple 8, 15, 17

 9. Oscar's dog house is shaped like a tent.  The slanted sides are both 5 feet long and the bottom of the house is 6 feet across.  What is the height of his dog house, in feet, at its tallest point? Choose: 3 4 4.5 5 Explanation Divide the doghouse into two right triangles. The 6 feet gets divided equally into 3 feet and 3 feet. Then use Pyth. Theorem or the triple, 3,4,5.

 10. Seth made a small rectangular table for his workroom.  The sides of the table are 36" and 18".  If the diagonal of the table measures 43", is the table square?  A table which is "square" has right angles at the corners. Choose: Yes No Explanation Use the Pythagorean Theorem to check for a right angle. a=36, b=18 and find c. When calculated, c = 40.2. Seth's table is NOT square.

 11. Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards, as shown in the diagram. What is the length of the diagonal, in yards, that Tanya runs? Choose:   50   60   70   80 Explanation Use the Pythagorean Theorem or use the Pythagorean Triple 3, 4, 5

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