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Pythagorean Theorem Practice Test
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Pythagorean Theorem Practice Test
Use the Pythagorean theorem, a² + b² = c², for right triangles. In this equation, c is the hypotenuse, the side opposite the right angle. Show your work for written problems. Round to the nearest tenth when needed.
Choose the Best Answer
Select one answer for each question.
1.A right triangle has legs measuring 5 inches and 12 inches. How long is its hypotenuse?
- 13 inches
- 17 inches
- 60 inches
- 119 inches
2.Which group of side lengths could make a right triangle?
- 6, 8, 10
- 4, 6, 9
- 5, 7, 10
- 3, 5, 7
3.The hypotenuse of a right triangle is 13 centimeters, and one leg is 5 centimeters. What is the length of the other leg?
- 8 centimeters
- 12 centimeters
- 18 centimeters
- 144 centimeters
4.For which triangles does the Pythagorean theorem apply?
- Only right triangles
- Every triangle
- Only equilateral triangles
- Only triangles with two equal sides
Find the Missing Side
Write an equation and show the steps you use.
5.A right triangle has legs of 7 feet and 24 feet. Find the hypotenuse.
6.A right triangle has a 26-meter hypotenuse and one leg that is 10 meters long. Find the other leg.
7.Logan sets a 17-foot ladder against a vertical wall. The ladder's base is 8 feet from the wall. How high up the wall does the ladder reach?
8.At a history museum, a square exhibit space has sides that are each 60 feet long. What is the straight-line distance across the space from one corner to the opposite corner? Give the exact answer and an approximation to the nearest tenth.
Apply the Theorem
Use the information in each problem to find the requested length or make a decision.
9.A rectangular museum display is 36 inches wide and 15 inches tall. Find the display's diagonal length.
10.Two museum staff members leave the same entrance. Chloe walks 24 yards west, while Owen walks 32 yards north. How far apart are they?
11.True or false: A triangle with side lengths 10, 24, and 26 is a right triangle. Verify your choice using the Pythagorean theorem.
TrueFalse
12.A rectangular museum gallery is 9 meters wide and 40 meters long. Find the distance diagonally from one corner of the gallery to the opposite corner.
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