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About Pythagorean Theorem — Class 8 IB

Apply the Pythagorean theorem and its converse to solve geometric problems. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 12). 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.

Pythagorean Theorem — solved examples for Class 8 IB

Example 1easy

A right triangle has legs of length 3 cm and 4 cm. What is the length of the hypotenuse?

Step-by-step solution

  1. c² = 3² + 4² = 9 + 16 = 25
  2. c = √25 = 5 cm

Answer: 5

Example 2medium

Find the distance between points \((-3, 2)\) and \((5, -4)\).

Step-by-step solution

  1. d = √((5+3)² + (−4−2)²) = √(64 + 36) = √100 = 10

Answer: 10

Example 3hard

A point \(P\) is 5 m from one end and 12 m from the other end of a 13 m long bridge. Is \(P\) on the bridge?
  1. A)Yes, P is on the bridge
  2. B)No, P is not on the bridge but it could be above or below it

Step-by-step solution

  1. 5 + 12 = 13 = length of bridge
  2. Since the distances sum to the bridge length, P lies on the bridge.

Answer: Yes, P is on the bridge

Practice questions on Pythagorean Theorem

  1. Q1.easy

    A right triangle has legs of length 6 cm and 8 cm. Find the hypotenuse.
    Show answer

    Answer: 10

    Hint: \(c^2 = 36 + 64\).

  2. Q2.easy

    The hypotenuse of a right triangle is 13 cm and one leg is 5 cm. Find the other leg.
    Show answer

    Answer: 12

    Hint: \(b^2 = c^2 - a^2 = 169 - 25\).

  3. Q3.easy

    Is a triangle with sides 7, 24, and 25 a right triangle?
    1. A)Yes
    2. B)No
    Show answer

    Answer: Yes

    Hint: Check if 7² + 24² = 25².

  4. Q4.medium

    An isosceles triangle has two equal sides of 13 cm and a base of 10 cm. Find the height of the triangle.
    Show answer

    Answer: 12

    Hint: The height bisects the base, creating a right triangle with hypotenuse 13 and base 5.

  5. Q5.medium

    A ship sails 15 km north and then 20 km east. How far is it from its starting point?
    Show answer

    Answer: 25

    Hint: North and east are perpendicular. Distance = \(\sqrt{15^2 + 20^2}\).

  6. Q6.medium

    The diagonal of a rectangular room is 15 m. If the room is 9 m long, what is its width?
    Show answer

    Answer: 12

    Hint: \(w = \sqrt{15^2 - 9^2}\).

  7. Q7.hard

    In a cuboid with dimensions 6 × 8 × 10, find the length of the space diagonal. Round to 1 decimal place.
    Show answer

    Answer: 14.1

    Hint: Space diagonal = \(\sqrt{6^2 + 8^2 + 10^2}\).

  8. Q8.hard

    Two buildings are 24 m apart. One is 7 m tall and the other is 17 m tall. Find the distance between their tops.
    Show answer

    Answer: 26

    Hint: Height difference = 10 m. Distance between tops = √(24² + 10²).

  9. Q9.hard

    A square pyramid has a base side of 12 cm and a slant height of 10 cm. Find the height of the pyramid.
    Show answer

    Answer: 8

    Hint: The slant height connects the apex to the midpoint of a base edge. Distance from centre to midpoint of edge = 6 cm.

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.