Advanced MathEasy–MediumLength of a rectangle from area and width (quadratic area)
Advanced Math practice question
A rectangle has an area of x² + 5x + 6 square units and a width of x + 2 units, where x > 0. What is the length of the rectangle when x = 4?
Answer: 7
Length = area ÷ width = (x + 2)(x + 3)/(x + 2) = x + 3. At x = 4, the length is 7. (Check: area 42 ÷ width 6 = 7.)
Common wrong answers
- If you answered 6
- 6 is the width at x = 4.
- If you answered 9
- 9 comes from x + 5, keeping the wrong factor.
- If you answered 42
- 42 is the area at x = 4, not the length.
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