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Quiz Chapter 13: The Pythagoras Theorem

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

10 questions · plays in fullscreen

Full Question List & Answer Key

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

1. A runner travels 8 km due North and then 15 km due East. How far is the runner from the starting point?

  1. 23 km
  2. 17 km
  3. 161 km
  4. 13 km
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Answer: B

Distance = √8² + 15² = √64 + 225 = √289 = 17 km.

2. 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.

3. In a right-angled triangle, the lengths of the two shorter sides are 6 cm and 8 cm. Find the length of the hypotenuse.

  1. 10 cm
  2. 14 cm
  3. 12 cm
  4. 100 cm
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Answer: A

c = √6² + 8² = √36 + 64 = √100 = 10 cm.

4. The diagonal of a square is 10 cm. Find the area of the square.

  1. 100 cm²
  2. 50 cm²
  3. 25 cm²
  4. 200 cm²
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Answer: B

Let side = s. s² + s² = 10² => 2s² = 100 => s² = 50. Area = s² = 50 cm².

5. What is the hypotenuse of a right-angled triangle?

  1. The shortest side
  2. The side opposite the acute angle
  3. The side opposite the 90° right angle
  4. The vertical height only
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Answer: C

The hypotenuse is the longest side of a right-angled triangle and lies directly opposite the 90° right angle.

6. If the hypotenuse of a right-angled triangle is 13 cm and one side is 5 cm, calculate the length of the third side.

  1. 8 cm
  2. 12 cm
  3. 18 cm
  4. 144 cm
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Answer: B

b = √13² - 5² = √169 - 25 = √144 = 12 cm.

7. In a rhombus with diagonal lengths 12 cm and 16 cm, find the length of one side of the rhombus.

  1. 10 cm
  2. 14 cm
  3. 20 cm
  4. 28 cm
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Answer: A

Diagonals of a rhombus bisect each other at right angles. Half diagonals are 6 cm and 8 cm. Side = √6² + 8² = √100 = 10 cm.

8. 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.

9. A ladder of length 5 m leans against a vertical wall. If the base of the ladder is 3 m away from the wall, how high up the wall does the ladder reach?

  1. 2 m
  2. 4 m
  3. 8 m
  4. 16 m
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Answer: B

Height = √5² - 3² = √25 - 9 = √16 = 4 m.

10. 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).

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