Practice Quiz

SAT Math

Category - Algebra and Functions

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The length of a rectangular playground is twice its width. If the length decreases by 2, and the width increases by 3, rectangular playground becomes a square playground. What is the perimeter of the rectangular playground?
  1. 10
  2. 20
  3. 30
  4. 40
  5. 50
Explanation
Answer: C - The perimeter of the rectangular playground is 30. Denote the length and width of the rectangular playground with l and w. The sides of the squared playground are l − 2 and w + 3, and must be equal. So, we have
l = 2w
l − 2 = w + 3
You can solve the system of equations by substituting l from the first equation into second equation.
2w − 2 = w + 3
2w − w = 2 + 3
w = 5
l = 2w = 2 × 5 = 10
Therefore, the perimeter of the rectangular playground is P = 2(l + w) = 2(10 + 5) = 30.
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