GMAT Focus EditionQuantitative ReasoningMedium
A civil engineer is designing a rectangular water reservoir. The length of the reservoir is 2 meters more than its width. If the area of the reservoir is 80 square meters, what is the width of the reservoir?
- A10 meters
- B8 meters
- C12 meters
- D6 meters
Show answer & explanationAnswer & explanation
Correct answer: B. 8 meters
Let the width be 'w'. Then the length 'l' is 'w + 2'. The area of a rectangle is length × width, so w(w + 2) = 80. This simplifies to w^2 + 2w - 80 = 0. Factoring the quadratic equation gives (w + 10)(w - 8) = 0. Since width cannot be negative, w = 8 meters.
Why the other options are wrong
- A. If width is 10, length is 12, area is 120, not 80.
- C. If width is 12, length is 14, area is 168, not 80.
- D. If width is 6, length is 8, area is 48, not 80.
Quadratic Equations (Geometric Problems)
Quadratic equations (ax^2 + bx + c = 0) arise in geometry when dealing with areas or volumes where dimensions are related in a way that involves squares of variables.
- Often involve finding dimensions (length, width, radius).
- Solutions may yield a positive and negative root, only positive is usually valid.
- Can be solved by factoring, quadratic formula, or completing the square.
Memory trick: Geometry's Dimensions Lead to Quadratic Solutions.