# Pythagoras' Theorem Exercise

## A self marking exercise on the application of Pythagoras' Theorem.

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Here are some questions which can be answered using Pythagoras' Theorem. You can earn a trophy if you get at least 9 questions correct. Each time you finish a question click the 'Check' button lower down the page to see if you got it right! Diagrams are not to scale.

 1. What is the name for the longest side of a right angled triangle? 2. What is the length of the longest side of a right angled triangle if the two shorter sides are 5cm and 12cm? cm 3. Find the length of AB to 1 decimal place. m 4. Find the length of EG to 1 decimal place. cm 5. Find the length of JK to 1 decimal place. mm 13cm17cm6. Find the height (h) of this isosceles triangle to one decimal place. cm 7. A rectangular swimming pool is 24m wide and 48m long. Calculate the length of a diagonal in metres to 1 decimal place. m 8. A ladder is 6m long. How far from the base of a wall should it be placed if it is to reach 5m up the wall? Give your answer in metres correct to 1 decimal place m 9. A tent guy line supports one of the upright tent poles. It runs from the top of the pole to a peg in the ground two and a half metres away from the base of the pole. If the guy line is 437cm long, how tall is the upright tent pole? Give your answer in centimetres correct to the nearest centimetre. cm 10. How long is the diagonal of an A4 size sheet of paper? The dimensions of A4 paper are 210 by 297 millimetres (8.3 inches × 11.7 inches). Give your answer in cm to one decimal place. cm 11. For international matches football pitches must be of regulation size. The goal lines must be between 64 and 75 metres (70 and 80 yards) long and the touchlines must be between 100 and 110 metres (110 and 120 yards).What is the difference between the length of the diagonal of the largest acceptable pitch and the length of the diagonal of the smallest acceptable pitch? Give your answer in metres to the nearest metre. m 5cm15cm19cm12. Find the perimeter of this parallelogram to one decimal place. cm
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This is Pythagoras' Theorem Exercise level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6 Level 7

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Did you enjoy doing this 'Pythagoras' Theorem Exercise' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept.

#### Suko Sujiko

Interactive number-based logic puzzles similar to those featuring in daily newspapers designed to develop numeracy skills. These puzzles are drag and drop and can earn you a Transum Trophy.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

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Gertrudis Jobs,

Thursday, October 27, 2022

"Level 6 - Question 9. I am standing in a rectangular hall, and my distances from three of the corners are 6 m, 9 m and 10 m. How far am I from the fourth corner? Give your answer correct to 3 significant figures.

[Transum: Thanks for your comment Gertrudis. Your answer is indeed correct if the order of measurements was different. You have made me realise that this question has three possible answers depending on the order of the measurements and which corner they refer to. This does make it a very interesting question. For the purposes of this exercise I have now added a diagram so the question only has one answer.]"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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## Description of Levels

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Level 0 - A 'whole number only' introductory set of questions

Level 1 - Finding the hypotenuse

Level 2 - Finding a shorter side

Level 3 - Mixed questions

Level 4 - Pythagoras coordinates

Level 5 - Mixed exercise

Level 6 - More than one triangle

Level 7 - Harder exercise

Pythagorean Probe - Levels 4 to 6 are quite a challenge.

Exam Style questions requiring an application of Pythagoras' Theorem and trigonometric ratios to find angles and lengths in right-angled triangles.

Three Dimensions - Three dimensional Pythagoras and trigonometry questions

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Pythagoras' Theorem

The area of the square on the hypotenuse of a right angled triangle is equal to the sum of the areas of the squares on the two shorter sides.

You may have learned the theorem using letters to stand for the lengths of the sides. The corners (vertices) of the right-angled triangle is labelled with capital (upper case) letters. The lengths of the sides opposite them are labelled with the corresponding small (lower case) letters.

Alternatively the sides of the right-angled triangle may me named using the capital letters of the two points they span.

As triangle can be labelled in many different ways it is probably best to remember the theorem by momorising the first diagram above.

To find the longest side (hypotenuse) of a right-angled triangle you square the two shorter sides, add together the results and then find the square root of this total.

To find a shorter side of a right-angled triangle you subtract the square of the other shorter side from the square of the hypotenuse and then find the square root of the answer.

### Example

AB2 = AC2 - BC2
AB2 = 4.72 - 4.12
AB2 = 22.09 - 16.81
AB2 = 5.28
AB = √5.28
AB = 2.3m (to one decimal place)

The diagrams aren't always the same way round. They could be rotated by any angle.

The right-angled triangles could be long and thin or short and not so thin.

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