Level 7-8 Shapes - Pythagoras

1. If the longest side of a right-angled triangle is c cm and the other sides are a cm and b cm, Pythagoras' Theorem states that .......

   • a² x b² = c²
   • (a + b)² = c²
   • a² + b² = c²
   • a² - b² = c²

2. In a right-angled triangle the sides forming the 90° angle are 6 cm and 8 cm. What is the length of the third side?

   • 10 cm
   • 12 cm
   • 14 cm
   • 16 cm

3. The following sets of numbers represent the lengths of the sides of a triangle. Which is not a right-angled triangle?

   • 15, 20, 25
   • 18, 24, 30
   • 16, 30, 36
   • 15, 36, 39

4. A triangle has sides of length 4 cm, 5 cm and 6 cm. Which of these statements is not true?

   • The longest side is opposite the 6 cm side
   • All three angles are acute
   • The triangle is scalene
   • The largest angle is 90°

5. The hypotenuse of a right-angled triangle is 26 cm. One of the shorter sides is 10 cm. How long is the third side?

   • 30 cm
   • 24 cm
   • 16 cm
   • 8 cm

6. A right-angled isosceles triangle has hypotenuse of length 15 cm. What are the angles at either end of the hypotenuse?

   • 15° and 75°
   • 30° and 60°
   • 45° and 45°
   • 20° and 70°

7. A rectangle has length 2.4 m and width 0.7 m. How long is its diagonal?

   • 2.0 m
   • 2.5 m
   • 3.0 m
   • 3.5 m

8. The foot of a ladder of length 3.75 m is 1.4 m away from a vertical wall. How high up the wall will the ladder reach (to the nearest 1 cm)?

   • 3.84 m
   • 3.48 m
   • 3.24 m
   • 3.18 m

9. The cross-section of a porch roof is an isosceles triangle with height 0.8 m and base 3.0 m. How long is each sloping roof section?

   • 3.1 m
   • 2.3 m
   • 1.9 m
   • 1.7 m

10. In a triangle, base 25 cm and height 12 cm, the perpendicular from the base to the opposite vertex divides the base in the ratio 3:2. How long are the other two sides (to 1dp)?

    • 15.6 cm and 19.2 cm
    • 16.3 cm and 18.9 cm
    • 15.6 cm and 16.3 cm
    • 18.9 cm and 19.2 cm

Quiz written by Hilary Wilson