The perimeter P of a rectangle with length l and width w is given by P = 2l + 2w. Which of the following expresses w in terms of P and l?

Question

Accepted Answer

B. w = (P − 2l)/2. Subtract 2l from both sides: P − 2l = 2w. Then divide both sides by 2: w = (P − 2l)/2. Choice A subtracts 2l but forgets to divide the whole remaining expression by 2. Choice C divides by 2 correctly but subtracts only l instead of 2l. Choice D divides only P by 2 (not the entire left side P − 2l), a failure to divide every term.

Answer

A. w = P − 2l — You correctly subtracted 2l from both sides to get P − 2l = 2w, but stopped there — you still need to divide the entire expression by 2.

Answer

C. w = (P − l)/2 — You divided by 2 correctly, but subtracted only l instead of 2l; the term paired with the length in P = 2l + 2w is 2l.

Answer

D. w = P/2 − 2l — You divided only the P by 2, not the whole left side — dividing P − 2l by 2 must halve both terms, giving P/2 − l.

Algebra practice question

Answer: B. w = (P − 2l)/2

Why the other answers are wrong

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