Worksheet Chapter 13: The Pythagoras Theorem

1. Calculate the length of the hypotenuse of a right-angled triangle with side lengths 12 cm and 16 cm.

2. True or False: If the sides of a triangle measure 6 cm, 8 cm, and 10 cm, then the triangle is a right-angled triangle.

3. Determine whether each of the following sets of side lengths forms a RIGHT-ANGLED, ACUTE-ANGLED, or OBTUSE-ANGLED triangle:
(a) 9 cm, 12 cm, 13 cm
(b) 7 cm, 24 cm, 25 cm
(c) 6 cm, 10 cm, 13 cm

4. An isosceles triangle PQR has side lengths PQ = PR = 15 cm and base QR = 18 cm.
(a) Calculate the perpendicular height from vertex P to base QR.
(b) Find the area of triangle PQR.

5. A rectangle has a length of 24 cm and a width of 10 cm.
(a) Calculate the length of its diagonal.
(b) Find the perimeter of one of the triangles formed by cutting the rectangle along its diagonal.

6. Two cyclists leave an intersection at the same time. Cyclist A travels West at 16 km/h, and Cyclist B travels South at 12 km/h.
(a) How far apart are the two cyclists after 2 hours?
(b) If they maintain the same speeds, after how many hours will they be 100 km apart?

7. A 13 m telephone pole casts a shadow on the ground. A support wire of length 15 m is attached from the top of the pole to a ground stake. How far is the stake from the base of the pole? (Express answer to 2 decimal places)

8. True or False: If c² > a² + b² for triangle sides a, b, and c (where c is the longest side), the angle opposite side c is an acute angle.

9. A right-angled trapezium ABCD has parallel sides AB = 12 cm and DC = 18 cm. The perpendicular height AD is 8 cm.
(a) Calculate the length of non-parallel side BC.
(b) Calculate the total perimeter of trapezium ABCD.

10. Fill in the blank: The longest side of a right-angled triangle which lies opposite the 90° angle is called the ________.