Question

enter the correct answer in the box.

an architect is designing a new building. he makes a model of the building such that the area of the rectangular base is \\(12x^2 - 11x - 5\\) and the length is \\(3x + 1\\).

what is the width of the model in terms of \\(x\\)?

Explanation:

Relate area, length, and width

Using the Simplifying Rational Expressions knowledge point

$$ \text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{12x^2 - 11x - 5}{3x + 1} $$

Factor the numerator

Using the Simplifying Rational Expressions knowledge point

$$ 12x^2 - 11x - 5 = (3x + 1)(4x - 5) $$

Divide to find the width

Using the Simplifying Rational Expressions knowledge point

$$ \text{Width} = \frac{(3x + 1)(4x - 5)}{3x + 1} = 4x - 5 $$

Answer:

An architect is designing a new building. He makes a model of the building such that the area of the rectangular base is \(12x^2 - 11x - 5\) and the length is \(3x + 1\).

What is the width of the model in terms of x?

<blank>\(4x - 5\)</blank>