GMAT Focus EditionQuantitative ReasoningHard
A civil engineer is designing a rectangular plot. The length of the plot is 5 meters more than its width. If the area of the plot is 84 square meters, what is the perimeter of the plot?
- A32 meters
- B44 meters
- C38 meters
- D50 meters
Show answer & explanationAnswer & explanation
Correct answer: C. 38 meters
Let the width of the plot be 'w' meters. Then the length is 'w + 5' meters. The area is length × width, so w(w + 5) = 84. This gives the quadratic equation w^2 + 5w - 84 = 0. Factoring the quadratic equation, we look for two numbers that multiply to -84 and add to 5. These are 12 and -7. So, (w + 12)(w - 7) = 0. Since width must be positive, w = 7 meters. The length is w + 5 = 7 + 5 = 12 meters. The perimeter is 2(length + width) = 2(12 + 7) = 2(19) = 38 meters.
Why the other options are wrong
- A. This could be a miscalculation of the dimensions or perimeter.
- B. This might result from an incorrect solution to the quadratic equation or an error in perimeter calculation.
- D. This is a plausible distractor if the dimensions are incorrectly derived.
Quadratic Equations (Geometric Problems)
Using quadratic equations to solve for unknown dimensions (like length or width) of geometric shapes when given information about area and relationships between sides.
- Area formulas for shapes often lead to quadratic expressions.
- Solving the quadratic equation provides possible values for dimensions.
- Only positive solutions are valid for physical dimensions.
Memory trick: Turn the words into algebra, solve the square, then find the edge!