Question 28841: Conditional Scaling of a Given Positive Area

Original question and givens

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 31/2>0 squared units. At corresponding positive length scale k=4/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

• G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 31/2>0 squared units. At corresponding positive length scale k=4/1, find the conditional scaled area. 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-area, scaled_area]

derived = [given_positive_area_times_squared_scale]

Similarity ORIGINAL scale numerator squared := mul(4, 4)

Similarity ORIGINAL scale numerator squared = 16

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

Similarity ORIGINAL scale denominator squared = 1

Similarity ORIGINAL given area numerator times p squared := mul(31, 16)

Similarity ORIGINAL given area numerator times p squared = 496

Similarity ORIGINAL given area denominator times q squared := mul(2, 1)

Similarity ORIGINAL given area denominator times q squared = 2

Similarity ORIGINAL scaled area fraction := div(496, 2)

Similarity ORIGINAL scaled area fraction = 248

source roles = [scaled_area, [31, 2, 4, 1]]

derived = [16, 1, 248/1]

Reverse checks

• S007 · 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.
• S006 · premise_and_result_audit — Recompute Similarity ORIGINAL scaled area fraction with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute Similarity ORIGINAL given area denominator times q squared with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute Similarity ORIGINAL given area numerator 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

248/1

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.