Question 1: Calculate the hypotenuse of a right-angled triangle with legs of 3 cm and 4 cm.

Answer: 5

Question 2: A ladder is leaning against a wall. The foot of the ladder is 6 m from the wall, and the ladder reaches 8 m up the wall. Calculate the length of the ladder.

Answer: 10

Question 3: A rectangle garden is 9 m long and 12 m wide. Find the length of the diagonal fence that runs across the garden.

Answer: 15

Question 4: In a right-angled triangle, one leg is 5 m, and the hypotenuse is 13 m. Find the length of the other leg.

Answer: 12

Question 5: A ramp rises 2 m vertically and has a length of 5 m along its slope. Is the ramp inclined at a right angle? Use Pythagoras to justify your answer.

Answer: Yes, because 2² + 4² = 20, and 5² = 25, fitting the Pythagoras relation.

Question 6: Construct a right-angled triangle with legs of 7 cm and 24 cm. Calculate the hypotenuse and verify your answer.

Answer: 25

Question 7: A square has a diagonal of about 14.14 cm. Find the length of each side, using Pythagoras.

Answer: 10

Question 8: A right-angled triangle has one leg of 9 m and a hypotenuse of 15 m. Find the other leg.

Answer: 12

Question 9: A surveyor measures a right-angled triangle where the horizontal distance is 40 m, and the direct distance to the point is 50 m. Find the height difference.

Answer: 30

Question 10: Identify the common mistake in solving for the hypotenuse when students forget to square the legs before adding. Describe how to correct it.

Answer: Mistake: Adding the legs directly instead of squaring and then adding. Correction: Square each leg, add the squares, then take the square root.