A rectangle has a height of 3 and a width of 3x2 + 4x. Express the area of the entire rectangle. Expression should be expanded. 332 43 Area =

Given:

A rectangle has a height of 3 and a width of 3x^2 + 4x. Express the area of the entire rectangle

Determine the area of the rectangle.

Formula for the area of the rectangle:

A = lw

Solution:

In order to determine the area of the rectangle, we must first find the width.

3x^2 + 4x

Factor out x.

x ( 3x + 4 )

Now we can equate the factored form to 0 and solve for x.

3x + 4 = 0

Transpose 4 to the other side of the equation, hence it must be taken to note that in transposing the number, the sign changes.

3x = -4

Divide both sides by 3 in order to determine the value of x.

3x/3 = -4/3

x = -4/3

Now we need to take the absolute value of the number, since we cannot have a negative width.

x = | -4/3 |

x = 4/3

Substitute the values of width and length to the formula for the area of the rectangle.

A = lw

A = (4/3)(3)

A = 4 square units

Final answer:

A = 4 square units