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SparkEd Math offers 60+ practice questions for Pythagoras 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.

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SparkEd Math uses visual step-by-step solutions for every Pythagoras 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 Pythagoras Theorem content aligned with the ICSE syllabus?

Yes, all Pythagoras Theorem questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Pythagoras Theorem — Class 9 ICSE (2025-26)

About Pythagoras Theorem — Class 9 ICSE

Prove the Pythagorean theorem and apply it to solve problems involving right triangles. This topic is part of the ICSE Class 9 mathematics syllabus (chapter: Chapter 10). On this page you can practice 50 questions across three difficulty levels — 10 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 Pythagoras Theorem

Introduction to Right-Angled Triangles and Pythagoras
The Pythagorean Theorem: The Core Concept
Applying Pythagoras: Finding Any Missing Side
Converse of Pythagoras Theorem & Pythagorean Triplets
Summary, Connections, and Exam Preparation

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

Pythagoras Theorem — solved examples for Class 9 ICSE

Example 1easy

Rina was solving a problem where she had a right-angled triangle PQR, with the right angle at Q. The lengths of sides PQ and PR were given as 8 cm and 17 cm respectively. She calculated the length of QR as follows:
8² + 17² = QR²
64 + 289 = QR²
353 = QR²
QR = √353 cm
What mistake did Rina make in her calculation?

A)She incorrectly squared 8.
B)She incorrectly squared 17.
C)She assumed PR was a leg, but it is the hypotenuse.
D)She should have subtracted the squares, not added them.

Step-by-step solution

The right angle is at Q, so the side opposite Q, which is PR, must be the hypotenuse.
According to the Pythagoras Theorem, (leg1)² + (leg2)² = (hypotenuse)².
Rina incorrectly set up the equation as PQ² + PR² = QR². The correct equation should be PQ² + QR² = PR², since PR is the hypotenuse.
Therefore, Rina made a mistake by assuming PR was a leg when it is the hypotenuse.

Answer: She assumed PR was a leg, but it is the hypotenuse.

Example 2medium

A right-angled triangle has legs of length 15 cm and 20 cm. What is the length of its hypotenuse?

A)25 cm
B)30 cm
C)35 cm
D)40 cm

Step-by-step solution

Let the legs be 'a' = 15 cm and 'b' = 20 cm, and the hypotenuse be 'c'.
According to Pythagoras theorem: a² + b² = c²
Substitute the values: 15² + 20² = c²
225 + 400 = c² => 625 = c² => c = √625 = 25 cm.

Answer: 25 cm

Example 3hard

In triangle ABC, AD is the altitude from A to BC. If AB = 13 cm, AC = 15 cm, and BC = 14 cm, find the length of AD.

A)10 cm
B)8 cm
C)12 cm
D)9 cm

Step-by-step solution

Let BD = x. Then DC = BC - BD = 14 - x.
In right-angled ΔABD, AB² = AD² + BD².
$13² = AD² + x² => 169 = AD² + x² (Eq 1)$
In right-angled ΔACD, AC² = AD² + CD².
$15² = AD² + (14 - x)² => 225 = AD² + 196 - 28x + x² (Eq 2)$
Substitute AD² from (Eq 1) into (Eq 2): 225 = (169 - x²) + 196 - 28x + x² => 225 = 365 - 28x => 28x = 140 => x = 5.
Substitute x = 5 into (Eq 1): AD² = 169 - 5² = 169 - 25 = 144 => AD = 12 cm.

Answer: 12 cm

Practice questions on Pythagoras Theorem

Q1.easy
In any right-angled triangle ABC, with the right angle at B, which of the following statements is always true regarding its sides?
1. A)AB is always shorter than BC.
2. B)AC is always the longest side.
3. C)The sum of the squares of AB and BC is equal to the square of AB.
4. D)The hypotenuse can sometimes be shorter than one of the legs.
Show answer
Answer: AC is always the longest side.
Hint: Remember the definition of the hypotenuse and its relationship to the other two sides in a right triangle.
Q2.easy
A rectangular field has a length of 24 meters and a width of 10 meters. What is the length of its diagonal?
1. A)26 meters
2. B)34 meters
3. C)14 meters
4. D)√576 meters
Show answer
Answer: 26 meters
Hint: A diagonal divides a rectangle into two right-angled triangles.
Q3.easy
An equilateral triangle has a side length of 12 cm. What is the length of its altitude?
1. A)6 cm
2. B)6√3 cm
3. C)12√3 cm
4. D)9 cm
Show answer
Answer: 6√3 cm
Hint: An altitude in an equilateral triangle bisects the base and forms two congruent right-angled triangles.
Q4.medium
The hypotenuse of a right-angled triangle is 26 cm, and one of its legs is 10 cm. What is the length of the other leg?
1. A)16 cm
2. B)20 cm
3. C)22 cm
4. D)24 cm
Show answer
Answer: 24 cm
Hint: Remember that the hypotenuse is always the longest side in a right-angled triangle. Use the theorem to find the unknown leg.
Q5.medium
Which of the following sets of numbers forms a Pythagorean triplet?
1. A)(6, 8, 9)
2. B)(5, 12, 13)
3. C)(7, 24, 26)
4. D)(8, 15, 16)
Show answer
Answer: (5, 12, 13)
Hint: A Pythagorean triplet consists of three positive integers a, b, and c, such that a² + b² = c². The largest number must be 'c'.
Q6.medium
A triangle has sides of length 7 cm, 8 cm, and 10 cm. Is this a right-angled triangle?
1. A)Yes
2. B)No
3. C)Cannot be determined
4. D)Only if the angles are known
Show answer
Answer: No
Hint: Use the converse of the Pythagorean theorem. If the square of the longest side is equal to the sum of the squares of the other two sides, then it is a right-angled triangle.
Q7.hard
The sides of a triangle are given as (x - 7) cm, x cm, and (x + 1) cm. If the triangle is a right-angled triangle, what is the value of x?
1. A)10
2. B)24
3. C)12
4. D)25
Show answer
Answer: 12
Hint: In a right-angled triangle, the hypotenuse is the longest side. Apply the Converse of Pythagoras Theorem.
Q8.hard
A rhombus has diagonals of length 24 cm and 10 cm. Find the perimeter of the rhombus.
1. A)52 cm
2. B)68 cm
3. C)72 cm
4. D)104 cm
Show answer
Answer: 52 cm
Hint: The diagonals of a rhombus bisect each other at right angles. This creates four congruent right-angled triangles.
Q9.hard
A ship leaves a port and sails 12 km due west. At the same time, another ship leaves the same port and sails 9 km due south. What is the shortest distance between the two ships at that moment?
1. A)15 km
2. B)18 km
3. C)21 km
4. D)25 km
Show answer
Answer: 15 km
Hint: Visualize the directions. West and South directions are perpendicular to each other, forming a right-angled triangle.

These are 9 of the 50 questions available for Pythagoras Theorem. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.