Edexcel IGCSE Math A 4.8.A Pythagoras theorem in 2D

Practise Pythagoras questions by identifying the hypotenuse, forming a squared-length equation and using the result in the wider diagram.

Exam points

Use Pythagoras' theorem to find a missing side in a right-angled triangle.
Identify the hypotenuse before deciding whether to add or subtract squared lengths.
Use the calculated length in perimeter, area or linked-triangle problems.

[Maximum number: 4]

The diagram shows a roof support.

Figure for Question 4.8.A Pythagoras' theorem in two dimensions question 1 — Edexcel IGCSE Math A Foundation

The roof support is made from four lengths of wood, A B, A C, B C and MC

A C=B C=9 \mathrm{~m} \quad A B=12 \mathrm{~m}

angle $A M C=90^{\circ}$
Lewis is going to buy lengths of wood to make the roof support.
The wood costs 21.50 euros per metre.
Each length of wood he buys has to be a whole number of metres.
Work out the total cost of the wood Lewis needs to buy.
Show your working clearly.

Diagram NOT accurately drawn
euros

$CM^2+\left(\frac{12}{2}\right)^2=9^2$ $CM=\sqrt{9^2-6^2}=\sqrt{45}=3\sqrt5=6.708\ldots$

Total wood length:
$6.708\ldots+9+9+12=36.708\ldots$

Cost:
$36.708\ldots\times21.50=789.23\ldots$

Using a 7 m purchased length for CM:
$(7+9+9+12)\times21.50=795.50$

Final answer:
795.50

SC B3 for awrt 789 if using $6.708\ldots$ directly.

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4.8.A Pythagoras' theorem in two dimensions question 1