  # Level 7-8 Shapes - Pythagoras 02

You've done a lot of work on shapes in KS3 Maths and we've already looked once at Pythagoras' theorem. But, it's such an important part of mathematics that we thought it deserved a second quiz.

Pythagoras Theorem is about a property of all triangles with a right-angle. If a triangle has one angle which is a right-angle (i.e. 90o) then there is a special relationship between the lengths of its three sides. The theorem states that the square of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the squares of the other two sides. It can be written as the following equation:

a2 + b2 = c2

See how well you understand Pythagoras' theorem in this quiz. Take your time and read each question carefully. And, one more thing... the diagrams are not drawn to scale. Good luck!

1.
What is the length of the hypotenuse (A) in the triangle below?
16 cm
20 cm
24 cm
28 cm
162 + 122 = 400
The square root of 400 is 20
2.
What is the length of the hypotenuse (A) in the triangle below?
17.9 cm
24.1 cm
30.4 cm
36.8 cm
The answer is given here to 3 significant figures
3.
What is the length of the hypotenuse (A) in the triangle below?
30.3 cm
32.1 cm
33.9 cm
36.7 cm
242 + 242 = 1,152
The square root of 1,152 is 33.9411....
4.
What is the length of the hypotenuse (A) in the triangle below?
6.54 cm
8.49 cm
10.22 cm
12.44 cm
62 + 62 = 72
The square root of 72 is 8.4852....
5.
What is the length of the hypotenuse (A) in the triangle below?
6.54 cm
8.49 cm
10.22 cm
12.44 cm
Well done if you spotted it is the same triangle as in question 4 but presented at a different rotation!
6.
What is the length of the hypotenuse (A) in the triangle below?
11.5 cm
13.4 cm
15.3 cm
17.8cm
62 + 122 = 180
The square root of 180 is 13.416.....
7.
What is the length of the side (A) in the triangle below?
4.7 cm
5.7 cm
6.7 cm
7.7 cm
62 + a2 = 92
36 + a2 = 81 so a2 = 45
The square root of 45 is 6.708....
8.
What is the length of the side (A) in the triangle below?
9.8 cm
10.9 cm
12.6 cm
13.4 cm
182 + a2 = 222
324 + a2 = 484 so a2 = 160
The square root of 160 is 12.649...
9.
The diagram below shows a ladder leaning against a vertical house wall. How far up the wall does the ladder reach?
4.4 m
4.8 m
5.2 m
5.6 m
4.22 + a2 = 72
17.64 + a2 = 49 so a2 = 31.36
The square root of 31.36 is 5.6
10.
What is the diagonal of the rectangular swimming pool in the picture below?
10.98 m
11.05 m
11.18 m
11.76 m
Think of the diagonal as the hypotenuse of a right angled triangle 