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Quiz Chapter 13: The Pythagoras Theorem

10 questions · Form 1 Mathematics Bab 13: The Pythagoras Theorem

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Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Which set of side lengths forms a right-angled triangle?

  1. 4 cm, 5 cm, 6 cm
  2. 5 cm, 10 cm, 12 cm
  3. 7 cm, 24 cm, 25 cm
  4. 8 cm, 12 cm, 15 cm
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Answer: C

Check 7² + 24² = 49 + 576 = 625. Longest side 25² = 625. Since 7² + 24² = 25², it forms a right-angled triangle.

2. The hypotenuse of a right-angled triangle is 25 cm. If one of the sides is 24 cm, find the area of the triangle.

  1. 84 cm²
  2. 168 cm²
  3. 300 cm²
  4. 150 cm²
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Answer: A

Other side = √25² - 24² = √625 - 576 = √49 = 7 cm. Area = 12 × 7 × 24 = 84 cm².

3. Calculate the perpendicular height of an isosceles triangle with side lengths 10 cm, 10 cm, and a base of 12 cm.

  1. 6 cm
  2. 8 cm
  3. 4 cm
  4. 16 cm
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Answer: B

The height bisects the base into two 6 cm segments. Height = √10² - 6² = √100 - 36 = √64 = 8 cm.

4. Find the perimeter of a right-angled triangle whose two perpendicular sides are 9 cm and 40 cm.

  1. 90 cm
  2. 81 cm
  3. 49 cm
  4. 41 cm
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Answer: A

Hypotenuse = √9² + 40² = √81 + 1600 = √1681 = 41 cm. Perimeter = 9 + 40 + 41 = 90 cm.

5. A right-angled isosceles triangle has two equal sides of length 7 cm. Find the length of the hypotenuse to 2 decimal places.

  1. 9.90 cm
  2. 14.00 cm
  3. 9.80 cm
  4. 11.40 cm
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Answer: A

Hypotenuse = √7² + 7² = √49 + 49 = √98 ≈ 9.90 cm.

6. Find the length of the diagonal of a rectangle measuring 9 cm by 12 cm.

  1. 21 cm
  2. 15 cm
  3. 18 cm
  4. 225 cm
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Answer: B

Diagonal = √9² + 12² = √81 + 144 = √225 = 15 cm.

7. A triangle has sides 9 cm, 12 cm, and 15 cm. What is the area of this triangle?

  1. 108 cm²
  2. 54 cm²
  3. 90 cm²
  4. 67.5 cm²
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Answer: B

Since 9² + 12² = 15², it is a right-angled triangle with perpendicular sides 9 cm and 12 cm. Area = 12 × 9 × 12 = 54 cm².

8. If the side lengths of a triangle satisfy c² > a² + b² (where c is the longest side), the triangle is classified as:

  1. An acute-angled triangle
  2. A right-angled triangle
  3. An obtuse-angled triangle
  4. An isosceles triangle
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Answer: C

According to the converse of Pythagoras Theorem, if c² > a² + b², the angle opposite side c is greater than 90° (obtuse).

9. Which of the following triple is NOT a Pythagorean triple?

  1. 3, 4, 5
  2. 5, 12, 13
  3. 6, 9, 12
  4. 8, 15, 17
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Answer: C

Check 6² + 9² = 36 + 81 = 117, whereas 12² = 144. Since 117 ≠ 144, 6, 9, 12 is not a Pythagorean triple.

10. A ship leaves a port and sails 12 miles West and then 5 miles South. What is the shortest distance back to port?

  1. 17 miles
  2. 13 miles
  3. 119 miles
  4. 15 miles
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Answer: B

Shortest distance = √12² + 5² = √144 + 25 = √169 = 13 miles.

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