Pythagorean Theorem Practice Tests

These Grade 8 Math practice tests cover right triangles, missing side lengths, square roots, exact radical answers, coordinate distance, the converse of the theorem, and real-world applications.

Skills covered

  • Using \(a^2+b^2=c^2\) to find a missing side
  • Identifying the hypotenuse and checking right triangles
  • Simplifying square roots and exact radical expressions
  • Applying the distance formula on the coordinate plane
  • Classifying triangles and solving ramp, ladder, diagonal, and travel problems

How to use these practice tests

Label the hypotenuse first, substitute the known lengths, solve for the missing side, and check that the hypotenuse is the longest side. Keep exact radical forms when a decimal is not requested.

For more Grade 8 Math practice, return to the Grade 8 Math category.

5. Test

Grade 8 Pythagorean Theorem Practice Tests

Practice Grade 8 Math questions about the Pythagorean Theorem, right triangles, square roots, distance, the converse, and real-world applications.

Choose the best answer for each question. Identify the hypotenuse, use the Pythagorean Theorem, and simplify exact radical answers when needed.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A ramp rises 6 feet and extends 8 feet horizontally. How long is the ramp?

Please select an answer first.

Correct answer: A

The correct answer is 1010 feet.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The ramp is the hypotenuse: sqrt62+82=10\\sqrt{6^2+8^2}=10 feet.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The ramp is the hypotenuse: sqrt62+82=10\\sqrt{6^2+8^2}=10 feet.

2. QuestionMultiple choice

A 13-foot ladder reaches a wall. Its base is 5 feet from the wall. How high does it reach?

Please select an answer first.

Correct answer: B

The correct answer is 1212 feet.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The height is sqrt132−52=sqrt144=12\\sqrt{13^2-5^2}=\\sqrt{144}=12 feet.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The height is sqrt132−52=sqrt144=12\\sqrt{13^2-5^2}=\\sqrt{144}=12 feet.

3. QuestionMultiple choice

A rectangular park is 30 yards by 40 yards. What is the distance across a diagonal?

Please select an answer first.

Correct answer: C

The correct answer is 5050 yards.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The diagonal is sqrt302+402=sqrt2500=50\\sqrt{30^2+40^2}=\\sqrt{2500}=50 yards.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The diagonal is sqrt302+402=sqrt2500=50\\sqrt{30^2+40^2}=\\sqrt{2500}=50 yards.

4. QuestionMultiple choice

A roof section has perpendicular lengths 9 feet and 12 feet. What is the supporting beam across them?

Please select an answer first.

Correct answer: D

The correct answer is 1515 feet.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The beam is the hypotenuse: sqrt92+122=15\\sqrt{9^2+12^2}=15 feet.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The beam is the hypotenuse: sqrt92+122=15\\sqrt{9^2+12^2}=15 feet.

5. QuestionMultiple choice

A television screen is 12 inches high and 16 inches wide. What is its diagonal?

Please select an answer first.

Correct answer: A

The correct answer is 2020 inches.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use d=sqrt122+162=sqrt400=20d=\\sqrt{12^2+16^2}=\\sqrt{400}=20 inches.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use d=sqrt122+162=sqrt400=20d=\\sqrt{12^2+16^2}=\\sqrt{400}=20 inches.

6. QuestionMultiple choice

A person walks 9 blocks east and 12 blocks north. How far is the direct route?

Please select an answer first.

Correct answer: B

The correct answer is 1515 blocks.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The direct route is sqrt92+122=15\\sqrt{9^2+12^2}=15 blocks.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The direct route is sqrt92+122=15\\sqrt{9^2+12^2}=15 blocks.

7. QuestionMultiple choice

A 17-foot rope runs from the top of a flagpole to a stake 8 feet from its base. How tall is the flagpole?

Please select an answer first.

Correct answer: C

The correct answer is 1515 feet.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The height is sqrt172−82=sqrt225=15\\sqrt{17^2-8^2}=\\sqrt{225}=15 feet.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The height is sqrt172−82=sqrt225=15\\sqrt{17^2-8^2}=\\sqrt{225}=15 feet.

8. QuestionMultiple choice

What is the diagonal of a square room with side length 10 feet?

Please select an answer first.

Correct answer: D

The correct answer is 10sqrt210\\sqrt{2} feet.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The diagonal is sqrt102+102=sqrt200=10sqrt2\\sqrt{10^2+10^2}=\\sqrt{200}=10\\sqrt{2} feet.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The diagonal is sqrt102+102=sqrt200=10sqrt2\\sqrt{10^2+10^2}=\\sqrt{200}=10\\sqrt{2} feet.

9. QuestionMultiple choice

An airplane travels 24 miles horizontally and rises 7 miles. What is the direct distance?

Please select an answer first.

Correct answer: A

The correct answer is 2525 miles.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The direct distance is sqrt242+72=sqrt625=25\\sqrt{24^2+7^2}=\\sqrt{625}=25 miles.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The direct distance is sqrt242+72=sqrt625=25\\sqrt{24^2+7^2}=\\sqrt{625}=25 miles.

10. QuestionMultiple choice

A wheelchair ramp is 13 feet long and rises 5 feet. How far does it extend horizontally?

Please select an answer first.

Correct answer: B

The correct answer is 1212 feet.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The horizontal length is sqrt132−52=sqrt144=12\\sqrt{13^2-5^2}=\\sqrt{144}=12 feet.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The horizontal length is sqrt132−52=sqrt144=12\\sqrt{13^2-5^2}=\\sqrt{144}=12 feet.

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