Pythagorean Theorem Question

📘 Introduction

Pythagorean Theorem Question The Pythagorean Theorem is one of the most important concepts in geometry. It is widely used in mathematics, physics, construction, and real-life problem solving. This theorem helps us find the relationship between the sides of a right-angled triangle.

If you are a Class 8, 9, or 10 student, mastering this topic is essential for exams. In this article, you will find easy, medium, and hard level questions, along with step-by-step solutions and a free worksheet PDF.Pythagorean Theorem Question

📐 Pythagorean Theorem Formula

$a^2 + b^2 = c^2$a2+b2=c2

$a$a

$b$b

$c = \sqrt{a^2 + b^2} \approx 21.21$c=a2+b2​≈21.21

$a^2 + b^2 = c^2 \approx 225.00 + 225.00 = 450.00$a2+b2=c2≈225.00+225.00=450.00abc

Where:

• a = base
• b = perpendicular
• c = hypotenuse (longest side)

👉 This formula is only applicable to right-angled triangles.Pythagorean Theorem Question

🟢 Basic Questions (Easy Level)

✔ Question 1

Find the hypotenuse when:
a = 3 cm, b = 4 cm

Solution:
c² = 3² + 4²
c² = 9 + 16 = 25
c = √25 = 5 cm

✔ Question 2

Find the missing side:
c = 13 cm, a = 5 cm

Solution:
b² = c² – a²
b² = 169 – 25 = 144
b = √144 = 12 cm

✔ Question 3

Find the hypotenuse:
a = 6 cm, b = 8 cm

Answer:
c = √(36 + 64) = √100 = 10 cm

🟡 Medium Level Questions

✔ Question 4

A ladder is leaning against a wall. The base is 9 m away from the wall and the height is 12 m. Find the length of the ladder.Pythagorean Theorem Question

Solution:
c² = 9² + 12²
c² = 81 + 144 = 225
c = √225 = 15 m

✔ Question 5

Find the diagonal of a rectangle with length 10 cm and width 24 cm.

Solution:
Diagonal = √(10² + 24²)
= √(100 + 576)
= √676 = 26 cm

✔ Question 6

Find the height of a triangle if hypotenuse = 25 cm and base = 7 cm.

Solution:
b² = 25² – 7²
b² = 625 – 49 = 576
b = √576 = 24 cm

🔴 Hard Questions

✔ Question 7

The coordinates of two points are (2,3) and (8,15). Find the distance between them.

Solution:
Distance = √[(8−2)² + (15−3)²]
= √(36 + 144)
= √180 = 6√5

✔ Question 8

A square has side length 10 cm. Find the length of its diagonal.

Solution:
Diagonal = √(10² + 10²)
= √200
= 10√2 cm

✔ Question 9

A person walks 6 km east and then 8 km north. Find the shortest distance from the starting point.

Solution:
Distance = √(6² + 8²)
= √(36 + 64)
= √100 = 10 km

🌍 Real-Life Applications

• 📏 Construction (measuring height and distance)
• 🧱 Architecture and design
• 🗺 Navigation and maps
• 🪜 Ladder problems
• 📐 Finding diagonals

📝 Practice Worksheet (Try Yourself)

1. a = 5, b = 12 → find c
2. c = 10, a = 6 → find b
3. a = 8, b = 15 → find c
4. A rectangle has sides 7 cm and 24 cm → find diagonal
5. Hypotenuse = 20 cm, base = 16 cm → find height

👉 Answers:

1. 13
2. 8
3. 17
4. 25 cm
5. 12 cm

📥 Download Worksheet PDF

🔗 Related Article

👉 Check also: Class 10 Maths Formulas PDF (All Chapters)

🏁 Conclusion

The Pythagorean Theorem is a powerful tool in mathematics that helps solve many real-world and exam-based problems. Practice different levels of questions regularly to gain confidence and improve your problem-solving skills.