ACT (Enhanced)MathematicsHard
A landscape architect is designing a rectangular flower bed. The length of the flower bed is 3 feet more than twice its width. If the perimeter of the flower bed is 30 feet, what is its width?
- A8 feet
- B4 feet
- C7 feet
- D6 feet
Show answer & explanationAnswer & explanation
Correct answer: B. 4 feet
Let 'w' be the width. The length 'l' is 2w + 3. The perimeter P = 2(l + w). Substitute the expressions for l and P: 30 = 2((2w + 3) + w). Simplify: 30 = 2(3w + 3). Divide by 2: 15 = 3w + 3. Subtract 3: 12 = 3w. Divide by 3: w = 4 feet.
Why the other options are wrong
- A. If width is 8, length is 2(8)+3=19. Perimeter is 2(8+19)=54, not 30.
- C. If width is 7, length is 2(7)+3=17. Perimeter is 2(7+17)=48, not 30.
- D. If width is 6, length is 2(6)+3=15. Perimeter is 2(6+15)=42, not 30.
Perimeter of a Rectangle
The total distance around the outside of a rectangle, calculated by P = 2(length + width) or P = 2l + 2w.
- Length and width are the dimensions.
- Units are linear (e.g., feet, meters).
- Used in fencing, framing, or outlining areas.
Memory trick: Word problems are puzzles, turn words into math equations.