The Baudhayana–Pythagoras Theorem — Practice

Question 1

Find the hypotenuse of a right triangle with legs 3 cm and 4 cm.

Accepted Answer

✦ Answer: c² = 3² + 4² = 9 + 16 = 25; c = 5 cm. (The famous 3-4-5 Pythagorean triple.)

Question 2

Is (5, 12, 13) a Pythagorean triple?

Accepted Answer

✦ Answer: 5² + 12² = 25 + 144 = 169 = 13². Yes, it IS a Pythagorean triple.

Question 3

A ladder is leaning against a wall. The foot is 9 m from the wall, and the top reaches 12 m up. How long is the ladder?

Accepted Answer

Step 1 — Identify the right triangle.
  Wall is vertical, ground is horizontal — they meet at 90°. The ladder is the hypotenuse.

Step 2 — Apply Pythagoras.
  Ladder² = 9² + 12² = 81 + 144 = 225
  Ladder = √225 = 15 m

Step 3 — Recognise the triple.
  (9, 12, 15) is 3 × (3, 4, 5) — a Pythagorean triple multiple.

Step 4 — Verify.
  9² + 12² = 81 + 144 = 225 = 15² ✓

✦ Answer: The ladder is 15 m long.

Question 4

A man walks 12 km east, then 5 km north. How far is he from the starting point (straight-line distance)?

Accepted Answer

Step 1 — Visualise.
  East and north are perpendicular. The path forms two legs of a right triangle. Straight-line distance is the hypotenuse.

Step 2 — Apply Pythagoras.
  Distance² = 12² + 5² = 144 + 25 = 169
  Distance = √169 = 13 km

Step 3 — Recognise (5, 12, 13) triple.
  This is a classic Pythagorean triple. Memorise it.

Step 4 — Sanity check.
  13 km is less than 17 km (12 + 5) — yes, the straight line is shorter than the walked path (triangle inequality).

✦ Answer: The man is 13 km from the starting point.

Question 5

A rectangular field is 80 m long and 60 m wide. A diagonal path is built across the field. (a) Find the length of the path. (b) If walking pace is 5 km/h, how long (in minutes) does it take to walk diagonally?

Accepted Answer

Part (a) — Find the diagonal.
  Diagonal² = 80² + 60²
            = 6400 + 3600
            = 10000
  Diagonal = √10000 = 100 m

Recognise the triple: (60, 80, 100) = 20 × (3, 4, 5). Confirmed.

Part (b) — Convert and compute time.
  Walking pace: 5 km/h = 5000 m/h
  Convert to m/min: 5000 / 60 ≈ 83.33 m/min
  
  Time = Distance / Speed
       = 100 / 83.33
       ≈ 1.2 minutes
  Or equivalently: 1 minute 12 seconds

Step — Verify.
  In 1.2 min at 83.33 m/min: 1.2 × 83.33 = 100 m ✓

✦ Answer: (a) Diagonal path = 100 m. (b) It takes about 1.2 minutes (1 min 12 s) to walk diagonally.

Practice — The Baudhayana–Pythagoras Theorem

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