Geometry and TrigonometryMediumRectangle area from a perimeter and a ratio
Geometry and Trigonometry practice question
A rectangle's length is twice its width, and its perimeter is 36. What is the area of the rectangle?
Answer: 72
Let the width be w; the length is 2w. Perimeter: 2(w + 2w) = 6w = 36, so w = 6 and the length is 12. Area = 12 × 6 = 72.
Common wrong answers
- If you answered 18
- 18 is 36/2, half the perimeter (length plus width), not the area.
- If you answered 36
- 36 is the perimeter itself, or 6 × 6 — a square. The rectangle is 6 by 12.
- If you answered 162
- 162 uses w = 9 (from 4w = 36), forgetting that the length is 2w, so the perimeter is 6w.
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