Question 28856: Squared Side Length under a Positive Scale

Original question and givens

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 37>0. At corresponding positive length scale k=1/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

• G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 37>0. At corresponding positive length scale k=1/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

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-similarity

Step-by-step derivation

source roles = [qf-similarity-scaled-squared-side, scaled_squared_side]

derived = [given_squared_side_times_squared_scale]

Similarity ORIGINAL scale numerator squared := mul(1, 1)

Similarity ORIGINAL scale numerator squared = 1

Similarity ORIGINAL scale denominator squared := mul(3, 3)

Similarity ORIGINAL scale denominator squared = 9

Similarity ORIGINAL given squared side times p squared := mul(37, 1)

Similarity ORIGINAL given squared side times p squared = 37

Similarity ORIGINAL scaled squared side over q squared := div(37, 9)

Similarity ORIGINAL scaled squared side over q squared = 37/9

source roles = [scaled_squared_side, [37, 1, 3]]

derived = [1, 9, 37/9]

Reverse checks

• S006 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.
• S005 · premise_and_result_audit — Recompute Similarity ORIGINAL scaled squared side over q squared with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute Similarity ORIGINAL given squared side times p squared with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute Similarity ORIGINAL scale denominator squared with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute Similarity ORIGINAL scale numerator squared with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.

Result

37/9

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.