14 Different Questions on Pythagoras Theorem for High Schools

Pythagoras theorem is actually a fundamental concept in mathematics every high school student will one way or the other comes across. In as much as that it is simple to deal with Pythagoras theorem questions, some still find it difficult to do so.

This content will provide a brief explanation about Pythagoras theorem and goes ahead to cover about 14 different questions for you. This concept is talked about when dealing with right triangles.

This is what it states; it states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be written as

cÂ² = aÂ² + bÂ² where â€˜câ€™ is the hypotenuse, and â€˜aâ€™ and â€˜bâ€™ are the other two sides of the right triangle.

## Let’s consider solving practical questions on Pythagoras theorem.

See the example below.

Suppose we have a right triangle with sides of length 3 cm and 4 cm. To find the length of the hypotenuse, we can use Pythagoras theorem as follows:

cÂ² = aÂ² + bÂ²

cÂ² = 3Â² + 4Â²

cÂ² = 9 + 16

cÂ² = 25

c = âˆš25

c = 5 cm

Therefore, the length of the hypotenuse is 5 cm.

Now it is your turn, take a look at these 14 questions on Pythagoras theorem. Make sure to share or discuss with your friends. For better results and understanding, form a group studies and solve them with the members.

To make this easier for you to solve, draw a triangle and indicate the sides mention in the questions on them. The slanted side of the triangle is the hypotenuse, the side opposite to the hypotenuse is the opposite and the third side is the adjacent.

### 14 Questions on Pythagoras theorem

1. Find the length of the hypotenuse of a right triangle with sides of length 6 cm and 8 cm.

2. Find the length of the shorter side of a right triangle with a hypotenuse of length 10 cm and the other side of length 8 cm.

3. Find the length of the longer side of a right triangle with a hypotenuse of length 13 cm and the other side of length 5 cm.

4. Find the length of the hypotenuse of a right triangle with sides of length 9 cm and 12 cm.

5. Find the length of the shorter side of a right triangle with a hypotenuse of length 15 cm and the other side of length 9 cm.

6. Find the length of the longer side of a right triangle with a hypotenuse of length 17 cm and the other side of length 8 cm.

7. A ladder is placed against a wall. The ladder is 10 meters long, and the base of the ladder is 6 meters away from the wall. How high up the wall does the ladder reach?

8. A kite is flown on a 60-meter long string. The string makes an angle of 45 degrees with the ground. How high above the ground is the kite?

9. A flagpole is 8 meters tall. A rope is tied to the top of the flagpole and anchored to the ground 6 meters away from the base of the pole. How long is the rope?

10. A right triangle has a hypotenuse of length 20 cm and one leg of length 16 cm. What is the length of the other leg?

11. A triangle has sides of length 5 cm, 12 cm, and 13 cm. Is this a right triangle? If so, what is the length of the hypotenuse?

12. A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?

13. A right triangle has a hypotenuse of length 25 cm and one leg of length 15 cm. What is the length of the other leg?

14. A right triangle has one leg of length 8 cm and the other leg of length 10 cm. What is the length of the hypotenuse?

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