# Lesson video

In progress...

Hi, I'm Miss Davies.

In this lesson we're going to be looking at applying Pythagoras's theorem to two triangles that share a side.

In this right-angled triangle we have a base of 15 metres and a hypotenuse of 25 metres, so we can apply Pythagoras's theorem.

This could be written as e squared add 225 is equal to 625.

This is the same as e squared equals 625 subtract 225, or e squared equals 400.

To find length e, we need to calculate the square root of 400, which is 20.

So length e is 20 metres.

We've now been asked to find the length labelled f.

To do this, we need to use that 20 metres.

We've got 20 squared add 35 squared is equal to f squared, as f is the hypotenuse of this right-hand right-angled triangle.

This can be rewritten as 400 add 1,225 is equal to f squared.

These sum to give 1,625.

To find length f, we need to calculate the square root of 1,625.

This is 40.

3 correct to one decimal place.

So length f is 40.

3 metres.

Here are some questions for you to try.

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

In part a, you find that x is eight centimetres.

They're going to use that in part b to find that y is 14.

4 centimetres.

In this next question we've been asked to calculate the length labelled r.

In order to do this, we need to first calculate the length labelled a.

To do this, we're going to apply Pythagoras's theorem to the left-hand triangle in which 17 centimetres is the hypotenuse, which will be our value for c, and 12 centimetres will be our value for b.

This can be rewritten as a squared add 144 is equal to 289.

This is the same as a squared is equal to 289 subtract 144.

A squared is equal to 145.

To find the length a, we need to calculate the square root of 145.

This is 12.

04 centimetres.

We can now calculate the length of side r.

Our hypotenuse is 29 centimetres.

04 as a, I have left it as the square root of 145, as this is more accurate.

The square root of 145 squared is 145.

We can rewrite this as r squared equals 841 subtract 145.

This is the same as 696.

To find the length labelled r, we're going to calculate the square root of 696.

This is 26.

38 to two decimal places.

Length r is 26.

38 centimetres.

Here is a question for you to try.

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

The exact value of x is two root 30, which is 10.

95 centimetres.

We use two root 30 to find the length of y, as it's more accurate.

In this question we have a quadrilateral that is made up of two right-angled triangles.

We are going to calculate the length AB.

This is the line that joins points A and B.

The first step is to calculate the length BD using Pythagoras's theorem.

Length BD is 10 centimetres.

We can now work out the length AB using Pythagoras's theorem where seven and 10 are the two shorter sides and AB is our hypotenuse.

The length AB is 12.

2 centimetres correct to one decimal place.

Here are some questions for you to try.

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

Your answers might be slightly off because you've used a rounded answer rather than the exact value of it.

This compound shape has been made up of two right-angled triangles.

The area of a triangle is found by multiplying the base by the height and dividing by two.

Therefore, we need to calculate the height of both of these triangles.

We are going to use Pythagoras's theorem to do that.

I've labelled the height as a.

The height of both of these triangles is 12.

04 centimetres.

The area of the left-hand triangle is worked out by calculating 12 multiplied by the square root of 145 divided by two.

I've used the square root of 145 rather than 12.

04, as it is more accurate.

The area of the left triangle is 72.

25 centimetres squared.

Next we're going to work out the base of the right-hand triangle using Pythagoras's theorem again.

I've used the square root of 145 rather than 12.

04, as it is more accurate.

The square root of 145 squared is 145.

The base of the right-hand triangle is 26.

38 centimetres.

I can now work out the area of the right triangle.

I'm going to calculate this by multiplying the square root of 696 by the square root of 145 and dividing this by two.

These two numbers are the accurate versions of the lengths.

The area of the right triangle is 158.

84 centimetres squared.

To find the total area of this compound shape, we are adding the two areas together.

72.

84 gives an area of 231.

09 centimetres squared.

Here are some questions for you to try.

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