Unit 3 Section 4 : Problems in Context

When solving problems using Pythagoras' Theorem, the key step is to draw a right-angled triangle.

Example Question
A ship sails 300 km due west and then 100 km due south.
At the end of this journey, how far is the ship from its starting position?

The first step is to draw a diagram showing the ship's starting position and the route it has taken:

We can see that the two parts of the journey form the two shorter sides of a right-angled triangle.
Now we need to use Pythagoras' Theorem to find the length of the hypotenuse, d.

Follow the steps below to work out each stage of the calculation, then click Click on this button below to see the correct answer to see whether you are correct.

Write down Pythagoras' Theorem with the relevant values :
Work out the squares of the two shorter sides :
Add together the two values on the right :
Find the square root of both sides :



Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

You will find it helpful to draw a diagram for each question showing the right-angled triangle.

Question 1
A hiker walks 300 m due north and then 400 m due east.

How far is the hiker now from her starting position?

Question 2
Two remote-controlled cars set off from the same position.
After a short time one has travelled 20 m due north and the other 15 m due east.

How far apart are the two cars?

Question 3
A room should have a rectangular floor, with sides of lengths 4 m and 5 m.
A builder wants to check that the room is a perfect rectangle and measures
the two diagonals of the room, which should be the same length.

How long should each diagonal be? Give your answer correct to 1 decimal place.

Question 4
Look at the triangle shown below.

Calculate the perimeter of the triangle, giving your answer correct to 1 decimal place.

Question 5
Look at the parallelogram below:

Calculate the perimeter of the parallelogram, giving your answer to 2 decimal places.

Question 6
Ron's dad says that Ron must not walk on the lawn. The lawn is a rectangle with sides of lengths 10 m and 16 m.
When his dad is looking, Ron walks from his house to the gate by walking along two edges of the lawn.
When his dad is not looking, Ron walks diagonally across the lawn.

How much further does Ron have to walk to get from the house to the gate when his dad is looking?
Give your answer correct to 2 decimal places.

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Produced by A.J. Reynolds February 2003