Test your understanding of the Pythagorean formula and how to find missing sides in right triangles.

Try to answer the questions before checking the answers at the bottom of the page.

Question 1

Find the hypotenuse:

Sides: \(6\) and \(8\)

a) \(10\)
b) \(12\)
c) \(14\)

Question 2

Find the missing side:

Hypotenuse \(= 10\)
Side \(= 6\)

a) \(6\)
b) \(8\)
c) \(9\)

Question 3

Find the missing side:

Hypotenuse \(= 13\)
Side \(= 5\)

a) \(10\)
b) \(11\)
c) \(12\)

Question 4

Find the hypotenuse:

Sides: \(5\) and \(12\)

a) \(13\)
b) \(14\)
c) \(15\)

Question 5

Find the hypotenuse:

Sides: \(1\) and \(1\)

a) \(1\)
b) \(\sqrt{2}\)
c) \(2\)

Question 6

Which side of a right triangle is the hypotenuse?

a) The shortest side
b) The side opposite the \(90^\circ\) angle
c) Either of the two legs

Question 7

Find the hypotenuse:

Sides: \(8\) and \(15\)

a) \(16\)
b) \(17\)
c) \(18\)

Question 8

Find the missing side:

Hypotenuse \(= 15\)
Side \(= 9\)

a) \(10\)
b) \(12\)
c) \(14\)

Question 9

Find the hypotenuse:

Sides: \(2\) and \(3\)

a) \(\sqrt{5}\)
b) \(\sqrt{10}\)
c) \(\sqrt{13}\)

Question 10

Which set of side lengths forms a right triangle?

a) \(6, 8, 10\)
b) \(5, 5, 9\)
c) \(4, 6, 8\)

Answers

1. a) \(10\)
2. b) \(8\)
3. c) \(12\)
4. a) \(13\)
5. b) \(\sqrt{2}\)
6. b) The side opposite the \(90^\circ\) angle
7. b) \(17\)
8. b) \(12\)
9. c) \(\sqrt{13}\)
10. a) \(6, 8, 10\)

Practice

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1. Pythagorean Formula
2. Pythagoras Theorem (a² + b² = c²) – Visual Proof 1
3. Pythagoras Theorem (a² + b² = c²) – Visual Proof 2
4. Pythagoras Theorem (Example)

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