Unit 12 · Class 8 IB MYP · MCQ Test
Pythagorean Theorem MCQ Test — Class 8 IB MYP
Practice 3 multiple-choice questions with instant answer reveal and explanations.
Pythagorean Theorem — MCQ Questions
1Which of the following is a Pythagorean triple?
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Answer: (5, 12, 13)
Hint: Check each: does a² + b² = c²?
Solution:
5² + 12² = 25 + 144 = 169 = 13² ✓
The others don't satisfy a² + b² = c².
2A right triangle has a perimeter of 30 cm and a hypotenuse of 13 cm. Find the two legs.
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Answer: 5 cm and 12 cm
Hint: Sum of legs = 30 − 13 = 17. Also a² + b² = 169. Use both equations.
Solution:
a + b = 17, a² + b² = 169
(a + b)² = a² + 2ab + b² = 289
2ab = 289 − 169 = 120, so ab = 60
a and b are roots of x² − 17x + 60 = 0
(x − 5)(x − 12) = 0, so legs are 5 and 12 cm
3Prove that a triangle with sides \(m^2 - n^2\), \(2mn\), and \(m^2 + n^2\) (where \(m > n > 0\)) is always a right triangle. If \(m = 3\) and \(n = 2\), what are the three sides?
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Answer: 5, 12, 13
Hint: Substitute m = 3, n = 2: sides are 9−4, 2(6), 9+4.
Solution:
m² − n² = 9 − 4 = 5
2mn = 2 × 3 × 2 = 12
m² + n² = 9 + 4 = 13
Check: 5² + 12² = 25 + 144 = 169 = 13² ✓
This formula always generates Pythagorean triples!
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Tips for Pythagorean Theorem MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Pythagorean Theorem MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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