Digital SATMath: AlgebraMedium
A city planner is designing a park. A rectangular section of the park has a perimeter of 120 meters. If the length of this section is 10 meters more than its width, what is the width of the rectangular section?
- A30 meters
- B55 meters
- C25 meters
- D35 meters
Show answer & explanationAnswer & explanation
Correct answer: C. 25 meters
Let the width be W and the length be L. We are given L = W + 10 and the perimeter P = 2L + 2W = 120. Substituting L into the perimeter equation gives 2(W + 10) + 2W = 120, which simplifies to 4W + 20 = 120. Solving for W gives W = 25 meters.
Why the other options are wrong
- A. This might be the result if L = W + 20 was used or an arithmetic error occurred.
- B. This might be the length if the perimeter was incorrectly divided or an addition error.
- D. This might be the length if the width was 25, or an error in solving the equation.
System of Linear Equations (Perimeter)
Using two linear equations to represent the relationships between the dimensions (length and width) and the perimeter of a rectangle, then solving for the unknown dimensions.
- Perimeter formula for a rectangle: P = 2L + 2W.
- One equation often relates length and width (e.g., L = W + x).
- Solve using substitution or elimination methods.
Memory trick: Perimeter's puzzle: Length and Width unlock.