Explore related knowledge and questions →
← Question derivation index · Original question batch
R0011-06330 · q-20261009-advance-20261013-r01-pythagorean-theorem-0030
Use a Euclidean right-triangle side-length model with strictly positive integer legs. a=15, b=20, with a perfect-square sum of squares. Find the positive integer hypotenuse c, not a negative root.
G001 — Use a Euclidean right-triangle side-length model with strictly positive integer legs. a=15, b=20, with a perfect-square sum of squares. Find the positive integer hypotenuse c, not a negative root.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
Euclidean right-side model;positive leg a=15
After
use the supplied right-angle premise:a²+b²=c²
Conditions: none
Use the declared Euclidean right-side model with positive legs.This finite numerical check is not a new universal proof of the Pythagorean theorem or an arbitrary affine-geometric bridge.
Rule: pythagorean_right_side_premise · Uses: G001
Before
known leg a squared := square(15)
After
known leg a squared = 225
Conditions: none
Square the complete known positive leg a.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
leg b squared := square(20)
After
leg b squared = 400
Conditions: none
Square the other positive leg b separately.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
sum of leg squares := sum(225, 400)
After
sum of leg squares = 625
Conditions: none
The sum of leg squares is the model's squared hypotenuse,not the hypotenuse itself.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
hypotenuse principal root squared := square(25)
After
hypotenuse principal root squared = 625
Conditions: none
Square the integer root to audit the positive-perfect-square premise,without rounded floating roots.
Rule: exact_rational_arithmetic · Uses: G001, S004
Before
root=25>0;root²=625=required square
After
unique positive length=25
Conditions: none
Matching the square still requires a positive length;a negative root is not a side length,and0 violates this nondegenerate positive-leg protocol.
Rule: positive_integer_length_root · Uses: G001, S005
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S005 · premise_and_result_audit — Recompute hypotenuse principal root squared with exact rational arithmetic, not rounded decimals.S004 · premise_and_result_audit — Recompute sum of leg squares with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute leg b squared with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute known leg a squared with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.25
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 4ab4490bfa7a99700ad9344cc5c9359945a54d9f53f92e4b67346bb7367b12aacandidate record SHA-256: 56ca413bd290f42a92c4aac847d0a497d0889d5fff69314aeaa34d8c7748ca8bsemantic review receipt SHA-256: b9bbc1c947f477a9c4bb5a579368ac5265f2da4572ce612c30f3633ecaf4ae80question-first witness SHA-256: 93f720df3ab3af13a792a3e6b443728e3c2a56276df839911f36569333236c55Lean: NOT_RUN · human review: NOT_PERFORMED