A garden has a triangular decking area, as shown in the diagram. The sides of the decking measure 9 metres, 12 metres and 15 metres. Determine whether the corner at C is a right angle. Justify your answer.(4 marks)
Identify the longest side and set up both calculations.
| a² + b² | c² |
|---|---|
| = 9² + 12²✓1 | = 15² |
In plain EnglishThe longest side is the hypotenuse — call it c.
Here c = 15 m, so the other two sides are a = 9 m and b = 12 m.
Write down that you are going to calculate a² + b² and c² separately. This earns the first mark.
Evaluate both sides and show them in a table.
| = 81 + 144 = 225 |
= 225✓2 |
In plain EnglishCalculate each side separately and place them side by side:
9² + 12² = 81 + 144 = 225 | 15² = 225
Both evaluations together earn the second mark.
9² + 12² = 81 + 144 = 225 | 15² = 225
Both evaluations together earn the second mark.
Make an explicit comparison.
a² + b² = c² (225 = 225)✓3
In plain EnglishYou must clearly state whether the two values are equal or not — SQA will not assume this from the numbers alone. Write:
a² + b² = c² (225 = 225)
This earns the third mark.
a² + b² = c² (225 = 225)
This earns the third mark.
Write a two-part conclusion in context.
∴ The angle at C is a right angle, so the decking is right-angled.✓4
In plain EnglishPart 1 — State what the comparison tells you about the angle:
"The angle at C is a right angle…"
Part 2 — Answer the actual question using the context:
"…so the decking is right-angled."
Both parts are needed for the fourth mark.
"The angle at C is a right angle…"
Part 2 — Answer the actual question using the context:
"…so the decking is right-angled."
Both parts are needed for the fourth mark.
⚠ Most marks are lost here. SQA requires an explicit comparison at mark 3 — just showing 225 and 225 without writing = is not enough. At mark 4, you must reference the angle and answer in context. "Yes" alone scores nothing.
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Your turn
Work out both sides, then choose the conclusion that would get full marks. Stuck? Tap Need a hint?
Past paper questions
Ready for exam-style questions? This collects every SQA past paper question on the converse of Pythagoras, with answers.
Converse of PythagorasEvery National 5 converse of Pythagoras question in one PDF, with answers.maths.scot · PDF Open ↗ (opens in a new tab)