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Pythagorean Theorem Practice
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Pythagorean Theorem Practice
Use the Pythagorean Theorem, a² + b² = c², for triangles with a 90° angle. Show your calculations for written problems. Give exact answers with radicals when needed, or round to the nearest tenth if asked.
Choose the Best Answer
1.A triangle has two perpendicular sides measuring 9 inches and 12 inches. What is the length of the side opposite the 90° angle?
- 13 in.
- 14 in.
- 15 in.
- 21 in.
2.Which set of three lengths forms a Pythagorean triple?
- (4, 5, 6)
- (7, 24, 25)
- (8, 10, 14)
- (9, 10, 12)
3.A triangle has perpendicular sides of 5 feet and 12 feet. What is the length of the side opposite the 90° angle?
- 11 ft
- 13 ft
- 15 ft
- 17 ft
4.A triangle has side lengths 8 cm, 15 cm, and 17 cm. What kind of triangle is it?
- Acute triangle
- Obtuse triangle
- Right triangle
- It cannot form a triangle
5.A triangle has a side opposite its 90° angle that measures 15 meters, and one of its other sides measures 9 meters. How long is the remaining side?
- 6 m
- 9 m
- 12 m
- 18 m
6.The side lengths of a triangle are 10, 24, and 26 units. Is the triangle a triangle with a 90° angle?
- Yes, because 10² + 24² = 26²
- Yes, because 10 + 24 = 26
- No, because 10² + 24² is less than 26²
- No, because its sides are not all equal
Solve and Explain
7.A triangle has a side opposite its 90° angle measuring 17 inches and another side measuring 8 inches. Find the third side. Show your work.
8.A triangle has side lengths 11, 60, and 61 centimeters. Use the converse of the Pythagorean Theorem to determine whether it has a 90° angle. Show a calculation.
9.A ramp rises 5 feet over a horizontal distance of 12 feet. How long is the ramp? Show your calculation.
10.A triangle has perpendicular sides of 7 centimeters and 10 centimeters. Find the length of the side opposite the 90° angle to the nearest tenth. Explain why the Pythagorean Theorem applies.
11.A rectangular field measures 9 meters by 40 meters. Find the length of a straight path across the field from one corner to the opposite corner. Show your work.
12.A triangle has side lengths 12 feet, 35 feet, and 37 feet. Does it have a 90° angle? Justify your answer by comparing the squares of its side lengths.
13.A triangle has a side opposite its 90° angle measuring 25 yards and another side measuring 7 yards. Find the length of the remaining side. Show your calculation.
3 printable pages
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