Advanced MathHardRatio of two rectangles' areas
Advanced Math practice question
Rectangle P has sides of length x and x + 4, and rectangle Q has sides of length x − 4 and x + 4, where x > 4. The ratio of P's area to Q's area can be written as x/(x − k), where k is a constant. What is the value of k?
Answer: 4
P's area is x(x + 4) and Q's is (x − 4)(x + 4). The common factor (x + 4) cancels, leaving x/(x − 4). So k = 4.
Common wrong answers
- If you answered 0
- 0 would make the ratio 1, but P is larger than Q.
- If you answered 16
- 16 is the constant in Q's expanded area, x² − 16.
- If you answered -4
- −4 would give x/(x + 4), keeping the cancelled factor.
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