In a cut-and-paste model, x²−14x+49 is changed into a smaller square. What is the side of the new square?

Correct answer: x−7; the correct reduced side

Correct answer: C. Recognize the expression as a perfect-square trinomial. The constant term 49 is 7², and the middle term is −14x=−2·x·7. Therefore x²−14x+49=(x−7)². In a cut-and-paste area model, the pieces rearrange to form a square whose side is x−7. Option A uses −14 as though it were the side, but −14 is the coefficient of x and must be divided by −2 to identify 7. Option B gives (x+7)², whose middle term is +14x, so its sign is wrong. Option D treats the whole constant 49 as a length, even though 49 is the square of the length 7. Memory cue: check both clues—constant equals the small side squared, and middle coefficient equals twice the signed side.