Question

The length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.Which function defines the area of the rectangle?Hint: A=l⋅w

Answer 1

The area of a rectangle is calculated using the formula:

`A=l* w`

where l is the length and w is the width.

The functions for the length and width are given to be:

`\begin{gathered} l(x)=2x+1 \\ w(x)=x+4 \end{gathered}`

Therefore, the area of the rectangle will be:

`A=(2x+1)(x+4)`

We can apply the FOIL Method:

`(a+b)(c+d)=ac+ad+bc+bd`

Therefore, we have:

`\begin{gathered} \left(2x+1\right)\left(x+4\right)=2x\cdot x+2x\cdot\:4+1\cdot\:x+1\cdot\:4 \\ =2x^2+8x+x+4 \end{gathered}`

Simplifying, the area is:

`a(x)=2x^2+9x+4`

The SECOND OPTION is correct.