Question

The area of a rectangle is represented by 3x^2-11x+6. Write an equivalent expression for the length and width. If x=12 what would the length and width be

Answer 1

• length: 3x-2
• width: x-3
• for x=12, length = 34; width = 9

Explanation:

Area is the product of length and width, so we expect to be looking for two factors that result in this quadratic.

The given quadratic can be factored as ...

3x^2 -11x +6 = (3x -2)(x -3)

Often, length is longer than width, so we can assign length the factor 3x-2 and width the factor x-3.

That is, expressions for length and width might be ...

• length: 3x -2
• width: x -3

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The values for x=12 are ...

• length = 3·12 -2 = 34
• width = 12 -3 = 9