Mathematics carries the highest weight in AISSEE — 150 of 300 marks in Class 6 and 200 of 400 marks in Class 9 — and it is also a key section of the RMS CET. Practise these 10 MCQs on Pythagoras Theorem, then check your answers and step-by-step solutions in the answer key at the end.
Quick facts: AISSEE 2027 will be held on Sunday, 31 January 2027. There is no negative marking, so attempt every question. Online applications are open until 2 December 2026 on exams.nta.nic.in/sainik-school-society.
Practice Questions
Q1. The two shorter sides of a right-angled triangle are 12 cm and 16 cm. What is the length of the hypotenuse?
(A) 28 cm
(B) 20 cm
(C) 21 cm
(D) 17 cm
Q2. The hypotenuse of a right triangle is 17 cm and one side is 8 cm. Find the other side.
(A) 9 cm
(B) 17 cm
(C) 25 cm
(D) 15 cm
Q3. Which of these is a Pythagorean triplet?
(A) (5, 6, 7)
(B) (8, 15, 17)
(C) (10, 12, 14)
(D) (2, 3, 4)
Q4. The two shorter sides of a right-angled triangle are 7 cm and 24 cm. What is the length of the hypotenuse?
(A) 31 cm
(B) 26 cm
(C) 27 cm
(D) 25 cm
Q5. The hypotenuse of a right triangle is 29 cm and one side is 20 cm. Find the other side.
(A) 9 cm
(B) 23 cm
(C) 21 cm
(D) 49 cm
Q6. A 13 m long ladder reaches a window 12 m high. How far is the foot of the ladder from the wall?
(A) 1 m
(B) 7 m
(C) 5 m
(D) 12 m
Q7. The two shorter sides of a right-angled triangle are 9 cm and 12 cm. What is the length of the hypotenuse?
(A) 15 cm
(B) 21 cm
(C) 16 cm
(D) 13 cm
Q8. The hypotenuse of a right triangle is 13 cm and one side is 5 cm. Find the other side.
(A) 8 cm
(B) 14 cm
(C) 18 cm
(D) 12 cm
Q9. A 25 m long ladder reaches a window 24 m high. How far is the foot of the ladder from the wall?
(A) 1 m
(B) 9 m
(C) 7 m
(D) 24 m
Q10. The hypotenuse of a right triangle is 10 cm and one side is 6 cm. Find the other side.
(A) 8 cm
(B) 4 cm
(C) 10 cm
(D) 16 cm
Answer Key with Explanations
(B) 20 cm — Hypotenuse = √(12² + 16²) = √400 = 20 cm.
(D) 15 cm — Other side = √(17² − 8²) = √225 = 15 cm.
(B) (8, 15, 17) — 8² + 15² = 289 = 17².
(D) 25 cm — Hypotenuse = √(7² + 24²) = √625 = 25 cm.
(C) 21 cm — Other side = √(29² − 20²) = √441 = 21 cm.
(C) 5 m — Distance = √(13² − 12²) = √25 = 5 m.
(A) 15 cm — Hypotenuse = √(9² + 12²) = √225 = 15 cm.
(D) 12 cm — Other side = √(13² − 5²) = √144 = 12 cm.
(C) 7 m — Distance = √(25² − 24²) = √49 = 7 m.
(A) 8 cm — Other side = √(10² − 6²) = √64 = 8 cm.
How did you score?
9–10 correct: excellent — move on to a full-length mock test. 6–8: good — revise the explanations of the questions you missed. Below 6: study this topic again from your NCERT book and retry these questions after two days.
Free AISSEE / RMS Mock Test
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