Practice | Baudhāyana–Pythagoras

Six AIMS practice sprints. Establish the conditions, preserve exact values and check units. Enter numerical answers without units; use the choices for exact radicals.

Sprint 1 — Square discovery

Progress: $\frac{0}{3}$ checked correctly

Q1. A square has area 18. Find the area of the square on its diagonal.Your numerical answer

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Q2. A square has side 10. Find its midpoint-square area.Your numerical answer

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Q3. Doubling a square’s side multiplies its area by what number?Your numerical answer

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Sprint 2 — Roots and bounds

Progress: $\frac{0}{4}$ checked correctly

Q1. An isosceles right triangle has equal legs 4. Its exact hypotenuse is…84√2√8

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Q2. Which statement is correct?√2=1.4141.415<√21.414<√2<1.415

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Q3. Hypotenuse √72, equal legs a: find a.Your numerical answer

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Q4. What proves √2 irrational?Its decimal does not terminateThe prime-factor parity contradictionIts first three decimals are 414

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Sprint 3 — Theorem and conditions

Progress: $\frac{0}{4}$ checked correctly

Q1. A right triangle has legs 5 and 12. Find the hypotenuse.Your numerical answer

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Q2. A right triangle has hypotenuse 17 and leg 8. Find the other leg.Your numerical answer

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Q3. An unmarked triangle has sides labelled 5,7,x. Can you immediately use x²=5²+7²?Yes, for all trianglesNo, the required right angle is not establishedYes, if x is drawn longest

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Q4. Sides 7,24,25 form a right triangle because…49+576=6257+24>25 alone25 is odd

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Sprint 4 — Triples and generation

Progress: $\frac{0}{4}$ checked correctly

Q1. Which triple is primitive?6,8,108,15,1715,36,39

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Q2. Scale (5,12,13) by 3. What is its hypotenuse?Your numerical answer

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Q3. In the odd-square generator with m=9, what is n?Your numerical answer

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Q4. Why does the generator miss (8,15,17)?It is not primitiveIt is not a right triangleNeither leg is 16

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Sprint 5 — Applications

Progress: $\frac{0}{4}$ checked correctly

Q1. Rhombus diagonals are 24 and 70. Find its side.Your numerical answer

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Q2. The source lotus has height 1 above water and horizontal reach 3. Find the depth under its stated assumptions.Your numerical answer

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Q3. Which grid-square area is impossible with integer vertices?235

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Q4. Equilateral triangle, side 6: its exact area is…1818√39√3

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Sprint 6 — Mixed Mastery

Progress: $\frac{0}{4}$ checked correctly

Q1. A square of area 49−25 has side…242√62

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Q2. Which hypothesis is essential for c=a√2 with equal legs a?The triangle is isosceles rightThe triangle is any isosceles triangleThe triangle is equilateral

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Q3. A right triangle has leg 40 and hypotenuse 41. Find the other leg.Your numerical answer

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Q4. A square has side vector (2,1) on a unit grid. Find its area.Your numerical answer

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Sprint 1 — Square discovery

Sprint 2 — Roots and bounds

Sprint 3 — Theorem and conditions

Sprint 4 — Triples and generation

Sprint 5 — Applications

Sprint 6 — Mixed Mastery

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