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Quiz Chapter 13: The Pythagoras Theorem

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

Question 1 of 10Score: 0

A square has a diagonal of length √50 cm. What is the side length of the square?

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 square has a diagonal of length √50 cm. What is the side length of the square?

  1. 25 cm
  2. 5 cm
  3. 10 cm
  4. 7.07 cm
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Answer: B

Let side = s. s² + s² = (√50)² => 2s² = 50 => s² = 25 => s = 5 cm.

2. 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.

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. 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.

5. 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.

6. 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.

7. 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.

8. Which of the following expression correctly states the Pythagoras Theorem for a right-angled triangle ABC with right angle at B?

  1. AC² = AB² + BC²
  2. AB² = AC² + BC²
  3. BC² = AB² + AC²
  4. AC = AB + BC
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Answer: A

Since the right angle is at B, the side opposite B is AC (the hypotenuse). Thus AC² = AB² + BC².

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. 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.

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