10 questions · Form 1 Mathematics Bab 13: The Pythagoras Theorem
A square has a diagonal of length √50 cm. What is the side length of the square?
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?
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.
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.
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?
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.
Answer: B
Diagonal = √(9² + 12²) = √(81 + 144) = √225 = 15 cm.
6. What is the hypotenuse of a right-angled triangle?
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.
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?
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?
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.
Answer: B
b = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.