Question

the area (in square inches) of a rectangle is given by the polynomial function \\(a(b) = b^2 + 13b + 36\\). if the width of the rectangle is \\((b + 9)\\) inches, what is the length?

Explanation:

Relate area, width, and length

Using the Geometric Polynomial Modeling knowledge point

$$ A(b) = \text{width} \times \text{length} $$

$$ b^2 + 13b + 36 = (b + 9) \times \text{length} $$

Factor the area trinomial

Using the Factoring Trinomials knowledge point

$$ b^2 + 13b + 36 = (b + 9)(b + 4) $$

Solve for the length

Using the Geometric Polynomial Modeling knowledge point

$$ (b + 9)(b + 4) = (b + 9) \times \text{length} $$

$$ \text{length} = b + 4 $$

Answer:

The area (in square inches) of a rectangle is given by the polynomial function \(A(b) = b^2 + 13b + 36\). If the width of the rectangle is \((b + 9)\) inches, what is the length? <blank>\(b + 4\)</blank> inches