  # Solve Complex problems Using Pythagoras' Theorem

In this worksheet, students will apply Pythagoras' theorem to solve more problems. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Eduqas, AQA, OCR, Pearson Edexcel,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:   #### Worksheet Overview We already know that our friend Pythagoras here, had the brain the size of a planet.

He must have as it is said that he never wrote any of his theories down. Let us put our thinking cap on the revise the theorem

Remember this theorem only works for right-angled triangles.

To find the hypotenuse (longer side) of a triangle 10² + 3² =  √109 = 10.44 cm to 2 decimal places

To find the shorter side length 9² - 7² =√32 = 5.66 to 2 decimal places

The key point here is to remember when to add and when to subtract.

We can apply this to solve all sorts of problems. However they may be presented.

Question 1

The diagonal of a square is 10 cm long.  What is the length of one side of the square? IF IN DOUBT, SKETCH IT OUT Now don't be tempted to think because this is a square it will be 10 cm.

Pythagoras gave us his theorem for a reason.

Here you can see a right angled triangle has been formed.

We know that ?² + ?² = 10² (100 cm)

The sides will both be the same length as we are looking at a square.

100 ÷ 2 = 50 cm² √ 50 cm² = 7.07 cm rounded to 2 decimal places

Question 2   You are always looking to sketch the situation out to turn a diagram into a right angles triangle.

In more complex problems you will need to draw on other knowledge too.

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