Pythagoras Theorem
1. Determine whether the triangle whose lengths of sides are 3 cm, 4 cm, 5 cm is a right-angled triangle.
2. Which of the following can be the sides of a right triangle?
- 2.5 cm,6.5 cm, 6 cm.
- 2 cm, 2 cm, 5 cm.
- 1.5 cm, 2cm, 2.5 cm.
In the case of right-angled triangles, identify the right angles.
3. PQR is a triangle, right-angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
4. ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.
5. Find the value of x in these diagrams.
6. A 15 m long ladder is leaning against a wall. The bottom of the ladder is 12 m from the base of where the wall meets the ground. At what height from the ground does the top of the ladder lean against the wall?
7. Angles Q and R of a ΔPQR are 25º and 65º. Write which of the following is true:
- PQ2 + QR2 = RP2
- PQ2 + RP2 = QR2
- RP2 + QR2 = PQ2
8. The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground, find the actual height of the tree.
9. Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
10. Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then find the distance between their tops.
11. The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
12. Calculate the area of an equilateral triangle inscribed in a circle of radius 6 cm.
13. Determine the area of the square inscribed in a circle with a circumference of 18.84 cm.
14. A square with a side of 2 m has a circle inscribed in it and in turn this circle has a square inscribed in it. If this square also has a circle inscribed in it, what is the area between the last square and the last circle.
15. If the sum of the sides of a right triangle is 49 cm and the hypotenuse is 41 cm, find the two sides.
16. In the right triangle ABC, point D is equidistant from AB and BC. Given that AD = 30, and DC = 40. Find lengths of sides AB and BC.
17. Prove that in a right triangle, the hypotenuse is twice the median drawn to the hypotenuse.
18. In a right triangle ABC, length of the medians to the sides AB and BC are 2√61 and √601 respectively. Find the length of its hypotenuse.
19. In the following diagram, PQRS is made from two right angled triangles. Work out the length of QR.
20. Here is a pattern made from right angled triangles. Work out the length x.
21. Here is a pyramid. Work out the height of the pyramid.
22. Here is a cuboid. Work out the length AG.
23. Form an equation and use it to work out the value of x.
24. In the following diagram of a circle, O is the centre and the radius is 12 cm. AB and EF are straight lines. Find the length of EF if the length of OP is 6 cm.
25. The rectangle PQRS represents the floor of a room. Roshan stands at point A. Calculate the distance of Roshan from
- the corner R of the room;
- the corner S of the room.
26. In the following right triangle, altitude BD = 9√10 cm and DC = 27√10 cm. Find the perimeter of the triangle.
