Pythagoras' theorem - in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Select the equation which shows Pythagoras' Theorem for this triangle.

\[{r^2} = {m^2} + {p^2}\]

\[{m^2} = {r^2} + {p^2}\]

\[{p^2} = {m^2} \times {r^2}\]

Calculate the length of the hypotenuse. Give your answer to 2 decimal places.

s = 12.04

s = 20.80

s = 20.81

t = 3.94

t = 3.95

t = 9.23

r = 40.76

r = 107.05

r = 107.06

Calculate \(x\) for this triangle. Give your answer to 2 decimal places.

\[x = 10.70\]

\[x = 10.72\]

\[x = 16.64\]

\[x = 8.08\]

\[x = 10.37\]

\[x = 10.38\]

\[x = 22.97\]

\[x = 22.98\]

\[x = 32.24\]

How far up the wall will the ladder reach? Give your answer to 2 d.p.

\[x = 3.84m\]

\[x = 5.93m\]

\[x = 5.94m\]

What is the distance between the points A(2, 1) and B(8, 9)?

14

10

5

How far apart are P( -3, 4) and Q(4, -2)? Give your answer correct to one decimal place.

6.9

9.3

9.2