In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other sides (adjacent and opposite). In triangle ABC shown as below.
Some cases of Pythagorean relationships are shown in the table below.
Class 6
1. The diagonal of a rectangular piece of cloth is 25 cm. If the width of this cloth is 25 cm, what is the size of the piece of cloth in square centimeters?
2. The area of a rectangle is 60 cm2. What is the length of the diagonal, in centimeters, if one side of the rectangle is 5 cm?
A. 25 B. 17 C. 13 D. 12
3. Mutiso required a set of three measurements on a rope to mark square corners on his farm. Which of the following sets of measurements would he use?
| A. 1.4 m |
2.0 m |
2.4 m |
| B. 1.5 m |
2.0 m |
2.5 m |
| C. 3.3 m |
4.0 m |
5.4 m |
| D. 0.9 m |
1.6 m |
2.5 m |
4. A carpenter used a 15 meter long ladder. One end of the ladder was placed 9 m away from a wall on level ground while the other end touched the top of the wall. What is the height of that wall?
A. 4 m B. 6 m C. 12 m D. 24 m
5. A rectangle measures 6 cm by 2.5 cm. What is the length of the diagonal in cm?
A. 17 B. 6.5 C. 15 D. 8.5
6. The area of a right-angled triangle is 84 cm2/ If the height of the triangle is 7 cm, what is the length of the longest side in cm?
A. 25 B. 24 C. 19 D. 12
7. The diagonal of a rectangle measures 6.5 cm. If one side of the rectangle measures 2.5 cm, what is the measure of the other side in cm?
A. 3 B. 6 C. 4 D. 2
8. From which of the following sets of lines can a right-angled triangle be drawn?
A. 3 cm, 4 cm, 7 cm B. 4 cm, 4 cm, 6 cm
C. 9 cm, 12 cm, 15 cm D. 9 cm, 16 cm, 25 cm
9. In the figure below, angle PQR is 900, QR = 8 cm, PR = RS = 10 cm and QRS is a straight line.
What is the area of triangle PRS in cm2?
A. 50 cm2 B. 54 cm2 C. 30 cm2 D. 24 cm2
10. The figure below represents a right-angled triangle ABC. The area of the triangle is 84 cm2 and side BC = 7 cm.
What is the length of side AC?
A. 31 cm B. 25 cm C. 24 cm D. 12 cm
11. Which one of the following sets of measurements will give a right-angled triangle?
| A. 0.5 cm |
1.2 cm |
1.3 cm |
| B. 0.9 cm |
1.6 cm |
2.5 cm |
| C. 0.1 cm |
0.3 cm |
0.4 cm |
| D. 0.3 cm |
0.4 cm |
2.5 cm |
12. The base of a right-angled triangle is 12 cm and the longest side is 13 cm. What is the area of the triangle?
A. 78 cm2 B. 60 cm2 C. 30 cm2 D. 25 cm2
