Question 6366: Ordered Leg Squares and Hypotenuse Square

Original question and givens

Use a Euclidean right-triangle side-length model with strictly positive integer legs. a=17, b=3. Give (a², b², a²+b²), retaining leg order; the last field is the model’s hypotenuse square.

• G001 — Use a Euclidean right-triangle side-length model with strictly positive integer legs. a=17, b=3. Give (a², b², a²+b²), retaining leg order; the last field is the model’s hypotenuse square.

Definition and scope

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.

• mko-euclid-pythagorean-theorem

Step-by-step derivation

Euclidean right-side model;positive leg a=17

use the supplied right-angle premise:a²+b²=c²

known leg a squared := square(17)

known leg a squared = 289

leg b squared := square(3)

leg b squared = 9

sum of leg squares := sum(289, 9)

sum of leg squares = 298

Reverse checks

• 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.

Result

(289, 9, 298)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.