Pythagoras' theorem: Practice questions


Pythagoras' theorem can be used to work out the length of the hypotenuse in a right-angled triangle:

  • Pythagoras' theorem states that in any right-angled triangle, the area of the square drawn on the hypotenuse is equal to the sum of the areas of the squares drawn on the two other sides.
  • The hypotenuse is the side of a right-angled triangle that is opposite the right angle. It is the longest side of the triangle.
  • The square of a number is that number multiplied by itself.
    For example, the square of 5 = 5² = 5 x 5 = 25.
  • The square root of a number is another number which when squared will equal the given number.
    For example, the square root of 64 = √64 = 8 (since 8 x 8 = 64).


Use the information above to help you answer these six questions related to using Pythagorasí theorem. The diagrams are not drawn to scale.

Question 1

What is the square of each of these numbers? Where necessary, give your answers to 2 decimal places.

a) 7     Square of 7 =

a) 25     Square of 25 =

a) 1.2     Square of 1.2 =

Question 2

What is the square of each of these numbers? Where necessary, give your answers to 2 decimal places.

a) 16     Square root of 16 =

a) 1296     Square root of 1296 =

a) 2.89     Square root of 2.89 =

Question 3

In each right-angled triangle, what is the length of side x? In each case, write 'yes' in the box beside the correct answer.

x = 25      x = 5      x = √ 7                         x = 10      x = 14      x = √ 28

What is the connection between the lengths of these triangles?

Question 4

Use Pythagoras' theorem, to work out if this statement is true or false: "In these diagrams, the diagonal of the rectangle is longer than the hypotenuse of the right-angled triangle." Give your answers correct to 1 decimal place.

Question 5

The diagram shows the dimensions of an aerial ropeway. The height of the tower is 20 metres and the anchor point is 35 metres from the base of the tower. Work out the length of the rope to 1 decimal place.

Question 6

A ship sails 24 kilometres due north and then 47 kilometres east. What is the distance of the ship from its starting point, rounded to the nearest kilometre?