NAME: ______ KEY PYTHAGOREAN THEOREM - WORKSHEET For each triangle find the missing length. Round your answer to the nearest tenth. Then find the area and the perimeter. [Triangle with sides 17, 19, and ?] [Triangle with sides 5, 13, and ?] [Triangle with sides 10, 20, and ?] [Triangle with sides 5, 14, and ?] See next page [written in blue ink] For #5-9 c is the hypotenuse of the right triangle ABC with sides a, b, c a = 12 ; b = 5 ; c = 13 12² + 5² = C² 144 + 25 = C² 169 = C² ± 13 = C a = 8 ; b = 6 ; c = 10 8² + b² = 10² 64 + b² = 100 b² = 36 b = ± 6 a = 15 ; b = 8 ; c = 17 15² + b² = 17² 225 + b² = 289 b² = 64 b = ± 8 a = 30 ; b = 40 ; c = 50 a² + 40² = 50² a² + 1600 = 2500 a² = 900 a = ± 30 a = 2√3 ; b = 2 ; c = 4 a² + 2² = 4² a² + 4 = 16 a² = 12 a = ± 2√3 Pythagorean Theorem Worksheet 17² + x² = 19² 289 + x² = 361 x² = 72 x = ± 8.48 x = 8.5 Area = ½ bh = ½ (17) (8.5) Area = 72.25 Perimeter = 19 + 17 + 8.5 = 44.5 5² + 13² = x² 25 + 169 = x² 194 = x² ± 13.9 = x 13.9 = x Area = ½ (13) (5) = 32.5 Perimeter = 5 + 13 + 13.9 = 31.9 x² + 10² = 20² x² + 100 = 400 x² = 300 x = ± 17.3 x = 17.3 Area = ½ (17.3) (10) = 86.5 Perimeter = 20 + 17.3 + 10 = 47.3 5² + 14² = x² 25 + 196 = x² 221 = x² ± 14.9 = x x = 14.9 Area = ½ (14) (5) = 35 Perimeter = 5 + 14 + 14.9 = 33.9 Find a third number so that the three numbers form a right triangle: i) 9, 41 9² + x² = 41² 81 + x² = 1681 x² = 1600 x = 40 ii) 13, 85 13² + x² = 85² 169 + x² = 7225 x² = 7056 x = 84 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. What is your answer? [Diagram of a right triangle with hypotenuse 13, one leg 5, and the other leg labeled x] x² + 5² = 13² x² + 25 = 169 x² = 144 x = 12 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? [Diagram of a right triangle with legs 8 and 5, and hypotenuse labeled x] x² + 5² = 8² x² + 25 = 64 x² = 39 x = ± √39 ≈ 6.244 6.2 miles 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? [Diagram of an isosceles triangle with base 6 and sides 5, with the height labeled x] 3² + x² = 5² 9 + x² = 25 x² = 16 x = 4 ft tall 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? 34² + 41² = x² 1156 + 1681 = x² 2837 = x² x = √2837 ≈ 53 meters A suitcase measures 24 inches long and the diagonal is 30 inches long. How much material is needed to cover one side of the suitcase? [Diagram of a rectangle with length 24 and diagonal 30, with the width labeled x] x² + 24² = 30² x² + 576 = 900 x² = 324 x = 18 Area = (18 x 24) = 432 in²

Pythagorean Theorem Worksheet

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