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

Answer: 5

Question 2: A ladder leans against a wall, forming a right triangle where the base is 6 meters and the ladder (hypotenuse) is 10 meters. Find the height at which the ladder touches the wall.

Answer: 8

Question 3: Construct a right-angled triangle on your grid with legs of 5 units and 12 units. Use the Pythagoras Theorem to find the hypotenuse.

Answer: 13

Question 4: A rectangular garden measures 8 meters by 15 meters. A diagonal path runs across the garden. Calculate the length of the diagonal path.

Answer: 17

Question 5: Explain why the Pythagoras Theorem only applies to right-angled triangles. Provide a brief reasoning.

Answer: Because the theorem relies on the relationship between the squares of the sides in a right triangle, which do not hold in triangles without a right angle.

Question 6: A triangle has sides of 7 units and 24 units, and the hypotenuse is to be found. Is this triangle a right-angled triangle? Show your reasoning.

Answer: Calculate 7² + 24² = 49 + 576 = 625. The hypotenuse squared is 625, so hypotenuse = 25 units. Since 25² = 625, yes, it's a right triangle.

Question 7: A right triangle has a hypotenuse of 13 units and one leg of 5 units. Find the length of the other leg.

Answer: 12

Question 8: Construct a right-angled triangle with hypotenuse 10 units and one leg of 6 units. Find the length of the other leg.

Answer: 8

Question 9: A square-based pyramid has a slant height of 14 meters and a base of 10 meters. Find the height of the pyramid, assuming the slant height forms a right triangle with the height and half the base length.

Answer: 12

Question 10: During a construction project, a worker measures a diagonal beam across a rectangle of 9 meters by 40 meters. Verify if the beam correctly measures the diagonal using the Pythagoras Theorem.

Answer: Check if 9² + 40² = 81 + 1600 = 1681. √1681 = 41. So, the diagonal should be 41 meters.

Question 11: Identify and correct the mistake in the following calculation: a triangle has legs 6 and 8 units, and the hypotenuse is calculated as 14 units.

Answer: Calculate 6² + 8² = 36 + 64 = 100. √100 = 10, not 14. The hypotenuse should be 10 units. The mistake was in calculating or assuming the hypotenuse as 14.