Set 3: Linear Equations

Choice A is correct. Choice A is the correct answer. 1. Define variables: Let $w$ be the width. Then length $l = 3 w$. 2. Perimeter formula: $P = 2 l + 2 w$ 3. Substitute: $32= 2(3 w) + 2 w$ 4. Simplify: $32= 6 w + 2 w \rightarrow 32 = 8 w$ 5. Divide by 8: $w = 4$ 6. Verify: Length is 12. $2(12) + 2(4) = 24 + 8 = 32$ ✓ Choice C is incorrect because this results from $4w = 32$ (forgetting to double sides). Choice D is incorrect because this is the length, not the width. Choice B is incorrect because this is half the perimeter.