Which equation correctly expresses the relationship for reverse extension between TA, TW, L, and E?

Which equation correctly expresses the relationship for reverse extension between TA, TW, L, and E?

• A. TW = TA × L ÷ (L − E)
• B. TA = TW × L ÷ (L − E)
• C. TA = TW × (L − E) ÷ L
• D. TW = TA × (L − E) ÷ L

Answer: (A)

When something length changes from its original length L to a shortened length L minus E, any quantity that scales with length needs to be adjusted by the ratio of the original length to the new length. In reverse extension, TW is the quantity that responds to that length change, so it must be TA multiplied by L divided by (L − E). That gives TW = TA × L ÷ (L − E). This form also makes intuitive sense: if there’s no extension (E = 0), TW equals TA, as expected since nothing has changed. If more length is removed (E grows), the denominator gets smaller, so TW becomes larger, reflecting the increased effect of the shortened length on the measurement. Other arrangements would not express TW as a direct scale of TA by the length-change ratio, or would invert the relationship, which wouldn’t match how the quantities relate when length decreases by E.

When something length changes from its original length L to a shortened length L minus E, any quantity that scales with length needs to be adjusted by the ratio of the original length to the new length. In reverse extension, TW is the quantity that responds to that length change, so it must be TA multiplied by L divided by (L − E). That gives TW = TA × L ÷ (L − E).

This form also makes intuitive sense: if there’s no extension (E = 0), TW equals TA, as expected since nothing has changed. If more length is removed (E grows), the denominator gets smaller, so TW becomes larger, reflecting the increased effect of the shortened length on the measurement.

Other arrangements would not express TW as a direct scale of TA by the length-change ratio, or would invert the relationship, which wouldn’t match how the quantities relate when length decreases by E.