How many practice questions are available for Pythagorean Theorem?

SparkEd Math offers 60+ practice questions for Pythagorean Theorem across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Pythagorean Theorem content free on SparkEd Math?

Yes! All Pythagorean Theorem content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Pythagorean Theorem differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Pythagorean Theorem problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Pythagorean Theorem content aligned with the CBSE syllabus?

Yes, all Pythagorean Theorem questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 8. The content follows the official curriculum structure and exam pattern.

Pythagorean Theorem — Class 8 CBSE (2025-26)

About Pythagorean Theorem — Class 8 CBSE

Prove and apply the Pythagorean theorem to solve right-triangle problems. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 9). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Pythagorean Theorem

Introduction to Right-Angled Triangles
Understanding the Pythagorean Theorem
Applying the Theorem to Find Unknown Sides
Pythagorean Triplets
Summary, Connections, and Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

Pythagorean Theorem — solved examples for Class 8 CBSE

Example 1easy

Which of the following statements about the Pythagorean theorem is TRUE?

A)It applies to all types of triangles.
B)It relates the sides of an equilateral triangle.
C)It is only applicable to right-angled triangles.
D)It states that the sum of angles in a triangle is 180°.

Step-by-step solution

The Pythagorean theorem establishes a fundamental relationship between the three sides of a right-angled triangle.
It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).
$a² + b² = c²$
Therefore, its application is strictly limited to right-angled triangles.

Answer: It is only applicable to right-angled triangles.

Example 2medium

In a right-angled triangle, the lengths of the two legs are 9 cm and 12 cm. What is the length of its hypotenuse?

A)15 cm
B)21 cm
C)7.5 cm
D)10.5 cm

Step-by-step solution

Let the legs be 'a' = 9 cm and 'b' = 12 cm. Let the hypotenuse be 'c'.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
$a² + b² = c²$
Substitute the values: 9² + 12² = c² => 81 + 144 = c² => 225 = c².
Take the square root: c = √225 = 15 cm.

Answer: 15 cm

Example 3hard

In a triangle ABC, if ∠B = 90° and AC is the longest side, which of the following statements is always true?

A)AC² = AB² - BC²
B)AB² = AC² + BC²
C)BC² + AB² = AC²
D)AB + BC = AC

Step-by-step solution

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).
Given that ∠B = 90°, the side opposite to ∠B is AC, which is the hypotenuse. The other two sides are AB and BC.
Therefore, according to the Pythagorean theorem,
$AB² + BC² = AC²$

Answer: BC² + AB² = AC²

Practice questions on Pythagorean Theorem

Q1.easy
Ravi was trying to find the length of the third side of a right-angled triangle with sides 5 cm and 12 cm. He wrote: 5² + x² = 12². What mistake did Ravi make?
1. A)He should have subtracted instead of added.
2. B)He incorrectly assumed 12 cm is a leg, when it could be the hypotenuse.
3. C)The theorem only works if all sides are known.
4. D)He used the wrong exponent; it should be 3 instead of 2.
Show answer
Answer: He incorrectly assumed 12 cm is a leg, when it could be the hypotenuse.
Hint: In a right-angled triangle, the hypotenuse is always the longest side and is isolated in the Pythagorean formula (c²). Consider if 12 cm could be the hypotenuse.
Q2.easy
Consider a right-angled triangle PQR, where the right angle is at Q. Which side represents the hypotenuse?
1. A)PQ
2. B)QR
3. C)PR
4. D)Any of the above, depending on the orientation.
Show answer
Answer: PR
Hint: Remember that the hypotenuse is always the side opposite the right angle in a right-angled triangle.
Q3.easy
Which of the following statements best describes a Pythagorean triplet?
1. A)A set of three odd numbers.
2. B)A set of three even numbers.
3. C)A set of three natural numbers a, b, c such that a² + b² = c².
4. D)A set of three numbers that can form any triangle.
Show answer
Answer: A set of three natural numbers a, b, c such that a² + b² = c².
Hint: Recall the definition of a Pythagorean triplet and how it relates to the Pythagorean theorem.
Q4.medium
A right-angled triangle has a hypotenuse of 25 cm and one of its legs is 7 cm. What is the length of the other leg?
1. A)18 cm
2. B)24 cm
3. C)20 cm
4. D)32 cm
Show answer
Answer: 24 cm
Hint: If you know the hypotenuse and one leg, you can rearrange the Pythagorean theorem to find the other leg.
Q5.medium
Which of the following sets of numbers forms a Pythagorean triplet?
1. A)(6, 8, 9)
2. B)(5, 12, 14)
3. C)(7, 24, 26)
4. D)(8, 15, 17)
Show answer
Answer: 8, 15, 17
Hint: For a triplet (a, b, c) to be Pythagorean, the square of the largest number (hypotenuse) must be equal to the sum of the squares of the other two numbers (legs).
Q6.medium
A ladder 17 m long rests against a vertical wall. The foot of the ladder is 8 m away from the base of the wall. How high up the wall does the ladder reach?
1. A)9 m
2. B)15 m
3. C)16 m
4. D)25 m
Show answer
Answer: 15 m
Hint: Visualize the situation as a right-angled triangle. The ladder is the hypotenuse, the distance from the wall is one leg, and the height reached is the other leg.
Q7.hard
A 15 m ladder is placed against a wall so that its foot is 9 m from the wall. The top of the ladder reaches a window. If the foot of the ladder is now pulled 3 m further away from the wall, how far will the top of the ladder slide down the wall?
1. A)3 m
2. B)4 m
3. C)5 m
4. D)6 m
Show answer
Answer: 4 m
Hint: Solve this in two parts: first find the initial height of the ladder, then find the new height after the foot is moved. The ladder's length remains constant.
Q8.hard
The diagonals of a rhombus are 24 cm and 10 cm. What is the perimeter of the rhombus?
1. A)26 cm
2. B)34 cm
3. C)48 cm
4. D)52 cm
Show answer
Answer: 52 cm
Hint: Remember that the diagonals of a rhombus bisect each other at right angles. This creates four right-angled triangles.
Q9.hard
The sides of a right-angled triangle are (x-1) cm, x cm, and (x+1) cm. Find the value of x.
1. A)4
2. B)5
3. C)6
4. D)7
Show answer
Answer: 4
Hint: In a right-angled triangle, the hypotenuse is always the longest side. Set up the Pythagorean equation with (x+1) as the hypotenuse.

These are 9 of the 60 questions available for Pythagorean Theorem. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.