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Junior Cycle Maths: Theorem of Pythagoras

How often Theorem of Pythagoras comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 4 of the last 5 Higher Level papers, most recently in 2026. most years

OL Asked on 4 of the last 5 Ordinary Level papers, most recently in 2026. most years

Theorem of Pythagoras, Higher Level(7 marks)

Quick ones on Theorem of Pythagoras.

(a)A right-angled triangle has shorter sides of 9 cm and 12 cm. How long is the hypotenuse?
  1. 21 cm
  2. 15 cm
  3. √63 cm
(b)The hypotenuse of a right-angled triangle is 13 cm and another side is 5 cm. How long is the third side?
  1. √194 cm
  2. 8 cm
  3. 12 cm
(c)Which set of side lengths makes a right-angled triangle?
  1. 8, 15, 17
  2. 5, 12, 14
  3. 6, 8, 11
Show the answers

(a) 15 cm

(b) 12 cm

(c) 8, 15, 17

Your turn: Higher Level questions on Theorem of Pythagoras.

Higher Level

Asked on 4 of the last 5 Higher Level papers, most recently in 2026. most years

Every paper, year by year

YearWhere it came up
2026Q11, Q13
2025Not asked
2024Q13
2023Q8, Q14
2022Q8

Links open the State Examinations Commission’s paper for that year.

More Theorem of Pythagoras questions

Theorem of Pythagoras, 2 marks

The theorem of Pythagoras can be used on…

  1. any triangle
  2. isosceles and equilateral triangles
  3. right-angled triangles only
Show the answer

right-angled triangles only

a² + b² = c² holds only when the angle opposite c is 90°. Before using it, check that the triangle has a right angle.

Ordinary Level

Asked on 4 of the last 5 Ordinary Level papers, most recently in 2026. most years

Every paper, year by year

YearWhere it came up
2026Q13
2025Not asked
2024Q11
2023Q13
2022Q11

Links open the State Examinations Commission’s paper for that year.

More Theorem of Pythagoras questions

Theorem of Pythagoras, 3 marks

A right-angled triangle has shorter sides of 6 cm and 8 cm. How long is the hypotenuse?

  1. 14 cm
  2. 100 cm
  3. 10 cm
Show the answer

10 cm

Pythagoras: c² = a² + b² = 36 + 64 = 100. Then c = √100 = 10 cm. Don't forget the square root at the end.

Theorem of Pythagoras, 2 marks

In a right-angled triangle, where is the hypotenuse?

  1. Opposite the smallest angle
  2. Opposite the right angle
  3. Next to the right angle
Show the answer

Opposite the right angle

The hypotenuse is always opposite the 90° angle, and it is always the longest side. It is c in c² = a² + b².

Theorem of Pythagoras, 3 marks

A right-angled triangle has hypotenuse 13 m and one other side 5 m. Find the third side.

  1. 12 m
  2. 8 m
  3. 13.9 m
Show the answer

12 m

You want a shorter side, so subtract: 13² − 5² = 169 − 25 = 144, and √144 = 12 m. Adding the squares only works for the hypotenuse.

Other Maths topics

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