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Maths Quiz - Level 7-8 Shapes - Pythagoras (Questions)

Right triangles unlock distances. Use Pythagoras’ theorem to find missing sides, check for right angles, and solve real problems involving ladders, ramps, and maps.

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Fascinating Fact:

If a square tile has a side of 8 cm, the diagonal across it measures √(8² + 8²) = √128 ≈ 11.3 cm.

In KS3 Maths, Pythagoras’ theorem links the sides of a right-angled triangle. You’ll calculate missing lengths, test whether triangles are right-angled, and apply the theorem to maps, ramps and real measurements.

Key Terms

Right-angled triangle: A triangle with one 90° angle.
Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.
Pythagoras’ theorem: In a right-angled triangle, a² + b² = c², where c is the hypotenuse.

Frequently Asked Questions (Click to see answers)

What is Pythagoras’ theorem in KS3?

Pythagoras’ theorem says that in any right-angled triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse: a² + b² = c².

How do I find a missing side using Pythagoras?

If the legs are 5 and 12, the hypotenuse is √(5² + 12²) = √169 = 13. If the hypotenuse and one leg are known, rearrange to a = √(c² ? b²).

How can I check if a triangle is right-angled?

Use the converse: if the longest side squared equals the sum of the other two squares (e.g., 7² + 24² = 25²), then the triangle is right-angled.

Try These Related Quizzes

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^o 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 three angles add up to 180^o
[ ]	All three angles are acute
[ ]	The triangle is scalene
[ ]	The largest angle is 90^o

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^o and 75^o
[ ]	30^o and 60^o
[ ]	45^o and 45^o
[ ]	20^o and 70^o

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

You can find more about this topic by visiting BBC Bitesize - Pythagoras

Maths Quiz - Level 7-8 Shapes - Pythagoras (Answers)

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
[x]	a² + b² = c²
[ ]	a² - b² = c²

Remember, Pythagoras' Theorem only applies to right-angled triangles

2.

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

[x]	10 cm
[ ]	12 cm
[ ]	14 cm
[ ]	16 cm

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

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
[x]	16, 30, 36
[ ]	15, 36, 39

Trial and error is a very useful tool in maths

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^o
[ ]	All three angles are acute
[ ]	The triangle is scalene
[x]	The largest angle is 90^o

(4 x 4) + (5 x 5) = 41 but 6 x 6 = 36 so the triangle cannot contain a right angle

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
[x]	24 cm
[ ]	16 cm
[ ]	8 cm

26² - 10² = 24²

6.

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

[ ]	15^o and 75^o
[ ]	30^o and 60^o
[x]	45^o and 45^o
[ ]	20^o and 70^o

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

7.

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

[ ]	2.0 m
[x]	2.5 m
[ ]	3.0 m
[ ]	3.5 m

The diagonal is the hypotenuse of a right-angled triangle

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
[x]	3.48 m
[ ]	3.24 m
[ ]	3.18 m

This assumes that the ground is perfectly level!

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
[x]	1.7 m

I hope you remembered the rules for isosceles triangles

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)?

[x]	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-angled triangles with bases 15 cm and 10 cm