Lesson video

Hi, I'm Miss Davies.

Today we're going to be finding the length of a hypotenuse using Pythagoras's theorem.

In the last lesson, we learned that Pythagoras's theorem states A squared plus B squared equals C squared.

Remember that C is always the hypotenuse.

The longest side that is opposite the right angle.

It doesn't matter which way round A and B are, because addition is commutative.

In this first example, we're calculating the hypotenuse.

Our two shorter sides, A and B are three centimetres and four centimetres.

If we substitute these into the formula, we get three squared plus four squared equal C squared.

We know that three squared is three times three, which is nine and four squared is 16.

These add to make 25.

The square root of 25 is 5.

So the length of the hypotenuse is 5 centimetres.

In this example, we're calculating the hypotenuse again.

With this question, the hypotenuse is the vertical line.

Our two shorter sides, A and B, are nine centimetres and 12 centimetres.

I'm going to label our hypotenuse as C.

The first thing we're going to do is write down Pythagoras's theorem.

We can then substitute the shorter length into the formula.

We get nine squared add 12 squared, equals C squared.

This is equivalent to 81 plus 144 equals C squared.

These add to make 225.

The square root of 225 is 15.

So the length of the hypotenuse is 15 centimetres.

Here are some questions for you to try.

Pause the video to complete your task and resume once you've finished.

Here are the answers.

For parts B, C and D, you might have rounded differently.

For example, for part B, you might have written 11.

18 centimetres.

The question specifies to round to three significant figures but all of your working out will still be correct.

Here is a question for you to try.

I would recommend you draw out a diagram to help you with this.

Pause the video to complete you task and resume once you finished.

Here is the answer.

I've drawn a diagram to help with the working out of this question.

Here's a question for you to try.

Pause the video to complete you task and resume the video once you've finished.

Here is the answer.

Teddy has squared the lengths of the sides incorrectly.

Nine squared is 81 and 12 squared is 144.

Here is a question for you to try.

Pause the video to complete your task and resume the video once you've finished.

Here is the answer.

You can draw a 10 centimetre line within in this rectangle because the diagonal length of is is 10.

6 centimetres.

In this example, we have a parallelogram.

And if you're asked to calculate its perimeter, we know that the horizontal lengths are both 18 centimetres, but we need to work out the diagonals.

How can we form a right angle triangle using the information we've been given? The distance between the parallel sides remains the same, so this is also 12 centimetres.

Now that we have a right angle triangle, we can apply Pythagoras's theorem.

Our shorter lengths, A and B, are five centimetres and 12 centimetres, which we can substitute into the formula to give 12 squared, add five squared equals C squared, where C represents the hypotenuse.

This is the same as 144 add 25 equals C squared.

These sum to a 169.

The square root of 169 is 13.

So the hypotenuse of this triangle is 13 centimetres.

We now know all of the lengths of the parallelogram so we can work out the perimeter by doing 18 add 13 add 18 add 13.

Which is the same as 31 add 31, or 62 centimetres.

Here is a question for you to try.

Pause the video to complete you task and resume the video, once you're finished.

Here is the answer.

The missing diagonal length of this trapezium is 5 centimetres.

This means the total perimeter is 22 centimetres.

Here is a question for you to try.

Pause the video to completed your task and resume the video once you've finished.

Here is the answer.

That is all for this lesson, thanks for watching.