Digital SATMath: AlgebraMedium
A farmer is fencing a rectangular plot of land. The length of the plot is 5 feet more than twice its width. If the perimeter of the plot is 100 feet, what is the width of the plot?
- A15 feet
- B30 feet
- C25 feet
- D20 feet
Show answer & explanationAnswer & explanation
Correct answer: A. 15 feet
Let 'w' be the width. The length 'l' is 2w + 5. The perimeter P = 2(l + w). Substitute the expressions: 100 = 2((2w + 5) + w). Simplify and solve for w: 100 = 2(3w + 5) => 50 = 3w + 5 => 45 = 3w => w = 15. The width is 15 feet.
Why the other options are wrong
- B. Incorrect. If w=30, l=65, P=2(30+65)=190, not 100.
- C. Incorrect. If w=25, l=55, P=2(25+55)=160, not 100.
- D. Incorrect. If w=20, l=45, P=2(20+45)=130, not 100.
Perimeter of a Rectangle
The total distance around the outside of a rectangle, calculated by summing the lengths of all four sides.
- Formula: P = 2(length + width) or P = 2l + 2w.
- In word problems, express length and width in terms of a single variable.
- Used in geometry and real-world applications like fencing or framing.
Memory trick: Geometry words become algebra lines, then solve for the shapes' secrets.