Advanced MathMediumDimension of a rectangle from an area expressed in x
Advanced Math practice question
A rectangular rug has sides of length (x − 3) metres and (x + 5) metres and covers an area of 20 square metres. What is the value of x?
Answer: 5
(x − 3)(x + 5) = 20 → x² + 2x − 15 = 20 → x² + 2x − 35 = 0 → (x + 7)(x − 5) = 0. Since x − 3 must be positive, x = 5.
Common wrong answers
- If you answered 2
- 2 is one side length (5 − 3), not x.
- If you answered 10
- 10 is the other side length (5 + 5).
- If you answered -7
- −7 is the other root, but it makes the sides negative.
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