Question

the diagram below shows the floor plan of a flower garden.
image of a rectangle with side lengths 2x + 4 and 3x - 1
if the area of the rectangle is represented by the expression (6x^2 + kx - 4), what is the value of (k)?
the value of (k) is ______.
options: 10, 12, -12, -10

Explanation:

Step1: Calculate the area of the rectangle

The area of a rectangle is given by the product of its length and width. Here, the length is \( 3x - 1 \) and the width is \( 2x + 4 \). So, we multiply these two binomials:
\[

$$\begin{align*} (3x - 1)(2x + 4)&=3x\times2x+3x\times4-1\times2x - 1\times4\\ &=6x^{2}+12x - 2x-4\\ &=6x^{2}+10x - 4 \end{align*}$$

\]

Step2: Compare with the given area expression

The given area expression is \( 6x^{2}+kx - 4 \). By comparing the coefficients of \( x \) in the expanded form (\( 6x^{2}+10x - 4 \)) and the given expression (\( 6x^{2}+kx - 4 \)), we can see that \( k = 10 \).

Answer:

10