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Pythagoras with Surds

Questions about right-angled triangles for which the answers should be surds in their simplest form

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This is level 3: Worded questions about real-life situations. You will be awarded a trophy if you get at least 7 answers correct and you do this activity online. Diagrams are not drawn to scale.

Click the √ button to get a square root sign in the answer area.

1

A picture frame around a family photograph is 8 inches tall and 12 inches wide. What is the length of the diagonal of the frame?

 in

2

A right-angled triangle has two sides of length 9 metres. What is the length of the hypotenuse?

 m

3

A rectangular field has a diagonal of 11 m and two sides of length 7 m. What are the lengths of the other two sides?

 m

4

A six metre ladder reaches up a tall wall. The base of the ladder is three metres from the base of the wall. How far up the wall does the ladder reach?

 m

5

An artist’s canvas has a diagonal of √15 inches, and the width is √7 inches. What is the height of the canvas?

 in

6

A roadside billboard is 6√2 ft tall and 8√3 ft wide. What is the diagonal measurement from the bottom-left to the top-right corner?

 ft

7

A bird starts from a church steeple and flies 10km due west. It then changes direction and flies 4km due south landing on an oak tree. How far is the tree from the steeple?

 km

8

On a sheet of graph paper a set of axes is drawn using a scale of one centimetre to represent one unit on both axes. What is the distance between (3,3) and (7,11)?

 cm

9

Find the perimeter of a right-angled triangle if it's hypotenuse is 13√5 mm and one of its other sides is 5√5 mm long.

 mm

10

Two right-angled triangles share a common side. Find the value of x.

Compound shape

 m

Check

This is Pythagoras with Surds level 3. You can also try:
Level 1 Level 2

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.

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Description of Levels

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Basic Pythagoras - Start with the basics of Pythagoras' Theorem.

Basic Surds - Here is the main exercise on Surds.

Level 1 - Where the length of the side to be found can be given as a surd

Level 2 - Where the length of the side to be found should be given as a surd in its simplified form

Level 3 - Worded questions about real-life situations

Probe - Using Pythagoras' theorem to find perimeters and areas.

More Pythagoras including lesson Starters, visual aids, investigations and self-marking exercises.

More Surds 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.

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Curriculum Reference

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

Example

Above is the video for the main exercise on Pythagoiras' Theorem. Don't forget that for the current exercise you will need to give your answer as a surd.

Below is a video called Surds which might help you revise the topic. It was made for the main Surds exercise.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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.

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