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This Shapes quiz looks at the special number relationship linking the lengths of the sides of a right triangle. This relationship is named after the Greek mathematician, Pythagoras. You may find it helpful to draw some diagrams.

Get your pencil and paper out and see how well you do in this quiz.

1.

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

This assumes that the ground is perfectly level!

2.

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

Split the triangle into two right triangles with bases 15 cm and 10 cm

3.

The following sets of numbers represent the lengths of the sides of a triangle. Which is not a right 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 three angles add up to 180°

All three angles are acute

The triangle is scalene

The largest angle is 90°

5.

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

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°

The side length is irrelevant. The only right-angled isosceles triangle has two angles of 45^{o}

7.

In a right 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

36 + 64 = 100; √100 = 10. The longest side in a right triangle is called the hypotenuse

8.

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

a^{2} x b^{2} = c^{2}

(a + b)^{2} = c^{2}

a^{2} + b^{2} = c^{2}

a^{2} - b^{2} = c^{2}

Remember, Pythagoras' Theorem only applies to right triangles

9.

The hypotenuse of a right 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

26^{2} - 10^{2} = 24^{2}

10.

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

The diagonal is the hypotenuse of a right triangle