Advanced MathEasy–MediumRecognising a quadratic from its description
Advanced Math practice question
A rectangular pen is to be built against a wall using 40 metres of fencing for the three open sides. If the side perpendicular to the wall is x metres, which function gives the pen's area A, in square metres?
- A. A(x) = x(40 − 2x)Correct
- B. A(x) = x(40 − x)
- C. A(x) = 2x(40 − x)
- D. A(x) = 40x
Answer: A. A(x) = x(40 − 2x)
Two sides of length x use 2x metres; the side parallel to the wall is 40 − 2x. Area = x(40 − 2x).
Why the other answers are wrong
- B. A(x) = x(40 − x)
- 40 − x subtracts only one perpendicular side; there are two.
- C. A(x) = 2x(40 − x)
- 2x(40 − x) doubles the wrong dimension.
- D. A(x) = 40x
- 40x ignores that fencing is shared among three sides.
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