AlgebraEasy–MediumInequality from a perimeter condition
Algebra practice question
A rectangle has sides of length x and x + 5. Which inequality describes all values of x for which the perimeter of the rectangle is greater than 50?
- A. x > 10Correct
- B. x > 12.5
- C. x ≥ 10
- D. x > 20
Answer: A. x > 10
Perimeter = 2(x + x + 5) = 4x + 10 > 50 → x > 10.
Why the other answers are wrong
- B. x > 12.5
- 12.5 comes from 4x > 50, forgetting the 10.
- C. x ≥ 10
- 'Greater than' excludes equality.
- D. x > 20
- 20 comes from 2x + 10 > 50, halving the perimeter.
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