A rectangular area model has a width of 3x and a length of 2.1x - 4.3x - 6.1. Jordan determined the area of the rectangle by finding the product of (3x) (2.1x^2 - 4.3x - 6.1).

Question

Complete the statement.
The area of the rectangle is ___.

Answer 1

To find the area of the rectangle, we can multiply the width by the length. The width is given as \( 3x \) and the length is given as \( 2.1x^2 - 4.3x - 6.1 \).

Thus, the area \( A \) can be expressed as:

\[ A = \text{width} \times \text{length} = 3x \times (2.1x^2 - 4.3x - 6.1) \]

Now, to calculate the area:

1. Distribute \( 3x \) across the polynomial:

\[ A = 3x \cdot 2.1x^2 + 3x \cdot (-4.3x) + 3x \cdot (-6.1) \]

2. Perform the multiplication:

\[ A = 6.3x^3 - 12.9x^2 - 18.3x \]

So, the area of the rectangle is:

\[ \boxed{6.3x^3 - 12.9x^2 - 18.3x} \]