Calculate the length of the hypotenuse c.(3 marks)
Write out Pythagoras' theorem and substitute.c² = a² + b²c² = 6² + 8²✓1
In plain EnglishAlways start by writing c² = a² + b², then replace a and b with the two shorter sides. This earns the first mark.
Work down to the value of c².c² = 100✓2
In plain EnglishSquare both numbers and add them: 36 + 64 = 100. Stop here and write c² = 100. This earns the second mark.
Square root to find c.c = √100c = 10 cm✓3
In plain Englishc = √100 = 10 cm. Always include the units in your final answer. This earns the third mark.
Calculate the length of the shorter side a.(3 marks)
Rearrange and substitute.a² = c² − b²a² = 15² − 9²✓1
In plain EnglishWhen finding a shorter side, rearrange to a² = c² − b² — you subtract the square of the known shorter side from the square of the hypotenuse. This earns the first mark.
Work down to the value of a².a² = 144✓2
In plain English15² − 9² = 225 − 81 = 144. Write a² = 144 clearly. This earns the second mark.
Square root to find a.a = √144a = 12 cm✓3
In plain Englisha = √144 = 12 cm. Don't forget the units. This earns the third mark.
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Past paper questions
Ready for exam-style questions? This collects every SQA past paper question on Pythagoras, with answers.
Pythagoras: mixed questionsEvery National 5 Pythagoras question in one PDF, with answers.maths.scot · PDF Open ↗ (opens in a new tab)