Extra Questions for Class 8 Maths Chapter 9: The Baudhayana-Pythagoras Theorem – HOTS

Original HOTS-level (Higher Order Thinking Skills) practice questions for Class 8 Maths Chapter 9 (The Baudhayana-Pythagoras Theorem), genuinely harder than the textbook exercise, using fresh numbers not found in the NCERT book. Full worked solutions included. These Class 8 Mathematics Chapter 9 important questions are handy for last-minute exam practice.

Last Updated: September 23, 2026

Q1 (Ladder problem). A 15 m ladder rests against a wall, its foot 9 m from the wall’s base. How high up the wall does it reach?
Solution: height² = 15² − 9² = 225 − 81 = 144 ⇒ height = 12 m.

Q2 (Generating a triple, Euclid-style). Using m = 3, n = 2, generate a Pythagorean triple via a = m²−n², b = 2mn, c = m²+n².
Solution: a = 9−4 = 5, b = 12, c = 13 ⇒ (5, 12, 13). Check: 25+144 = 169 = 13². ✓

Q3 (Assertion–Reason). Assertion (A): (9, 12, 15) is a primitive Pythagorean triple. Reason (R): A triple is primitive if the HCF of the three numbers is 1.
Solution: HCF(9,12,15) = 3 ≠ 1, so (9,12,15) is not primitive — it’s 3×(3,4,5). Assertion is false; Reason is true (R correctly defines primitivity, it’s just that the triple in A fails that test).

Q4 (Reverse problem). A rectangle has diagonal 25 cm and one side 24 cm. Find its perimeter.
Solution: Other side² = 25² − 24² = 625 − 576 = 49 ⇒ other side = 7 cm. Perimeter = 2(24+7) = 62 cm.

Q5 (Multi-step, sliding ladder). A 17 m ladder leans against a wall reaching 15 m up. If the foot of the ladder is pulled out by 7 m, how far down the wall does the top slide?
Solution: Initial foot distance = √(17²−15²) = √64 = 8 m. New foot distance = 8+7 = 15 m. New height = √(17²−15²) = √64 = 8 m. The top slides down from 15 m to 8 m — a drop of 7 m.

Q6 (Spot the error). A student claims that doubling all three sides of a right triangle also doubles its area. Check this claim.
Solution: Original area = ½ab. Doubled sides: ½(2a)(2b) = 4 × (½ab), i.e. 4 times the original area, not 2 times. The student’s claim is false.

Q7 (Lattice grid extension). Can a square of area 10 square units be drawn on a lattice/dot grid? If yes, give the vector.
Solution: 10 = 1²+3² = 1+9. Yes — use the vector (1,3).

Q8 (Proof, similar triangles). Prove that dropping an altitude from the right angle to the hypotenuse of a right triangle divides it into two smaller triangles, each similar to the original.
Solution: Let ▵ABC be right-angled at A, with altitude AD drawn to hypotenuse BC. In ▵ABD and ▵CBA: ∠ADB = ∠BAC = 90°, and ∠B is common to both, so ▵ABD ∼ ▵CBA (AA similarity). By the same reasoning with ∠C common, ▵ACD ∼ ▵BCA. Hence all three triangles — ▵ABD, ▵ACD and ▵ABC — are similar to one another.

Q9 (Integer hypotenuse). A right triangle has integer hypotenuse 25 units. List every possible pair of positive integer legs.
Solution: Need a²+b² = 625 with positive integers a ≤ b. 7²+24² = 49+576 = 625 ✓. 15²+20² = 225+400 = 625 ✓. So the pairs are (7, 24) — a primitive triple — and (15, 20), which is 5×(3,4,5).

Q10 (Real-world application). A rectangular TV screen advertised as “50 inches” (measured along its diagonal) has a width-to-height ratio of 16:9. Find its actual width and height, to 1 decimal place.
Solution: Let width = 16k, height = 9k. Diagonal² = (16k)²+(9k)² = 337k² = 50² = 2500 ⇒ k² = 2500/337 ≈ 7.418 ⇒ k ≈ 2.724. Width = 16k ≈ 43.6 in; Height = 9k ≈ 24.5 in.

More on This Chapter

See also: NCERT Solutions for Class 8 Maths Chapter 9, Class 8 Maths NCERT Book and the Class 8 Maths Formulas Handbook.

Revision Notes: Revision Notes for Class 8 Maths Chapter 9

Frequently Asked Questions

How can the Pythagoras theorem be used to find the length of a ladder needed to reach a certain height, given the distance of its base from the wall?
Since the wall, ground, and ladder form a right triangle with the ladder as hypotenuse, the ladder length can be calculated by taking the square root of the sum of the squares of the height and base distance.

How does the Pythagoras theorem help find the diagonal of a rectangle when only its length and breadth are known?
The diagonal, along with the length and breadth, forms a right triangle, so the diagonal can be found by taking the square root of the sum of the squares of the length and the breadth.

Written by Satish

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