ACT (Enhanced)MathematicsMedium
A farmer is planning a new rectangular pasture. He has 400 meters of fencing available. If he wants to maximize the area of the pasture, what should be the dimensions of the rectangle?
- A80 m by 120 m
- B100 m by 100 m
- C90 m by 110 m
- D120 m by 80 m
Show answer & explanationAnswer & explanation
Correct answer: B. 100 m by 100 m
To maximize the area of a rectangle given a fixed perimeter, the shape should be a square. With 400 meters of fencing, each side of the square would be 400 / 4 = 100 meters.
Why the other options are wrong
- A. This rectangle has a perimeter of 400m but a smaller area (9600 sq m) than a square.
- C. This rectangle has a perimeter of 400m but a smaller area (9900 sq m) than a square.
- D. This is the same as option A, just with swapped dimensions.
Maximizing Rectangular Area
For a fixed perimeter, the rectangle with the maximum area is a square. All sides are equal.
- Perimeter = 2(length + width).
- Area = length × width.
- When length = width, the shape is a square, and area is maximized.
Memory trick: Square is 'S'uperior for 'S'urface area with a fixed 'S'ide length when maximizing.