Question

The length of a rectangle is represented by the function L(x) = 5x. The width of that same rectangle is represented by the function W(x) = 2x^2 − 4x + 13. Which of the following shows the area of the rectangle in terms of x?

Answer 1

Remember that the area of a rectangle is the length of the rectangle multiplied by the width of the rectangle.

In this case, we could say (where $A(x)$ is the area of the rectangle):

$A(x) = L(x) \cdot W(x)$

Substituting the values the problem gave us for $L(x)$ and $W(x)$, we can find the formula for $A$ in terms of $x$, which is:

$A(x) = (5x) \cdot (2x^2 - 4x + 13) = (10x^3 - 20x^2 + 65x)$

The formula for the area of the rectangle would be A(x) = 10x³ - 20x² + 65x.

Answer 2

Recall that Rectangle area is the multiple of W*L

So Multiply both equations, you will get the area in terms of x.

The answer would be => A(x)=10x^3-20x^2+65x

Hope this helps :)