Question

an engineer is designing a building and wants rectangular spaces to maintain a ratio of 2 to 3. for any measurement value x, the length and width of the rectangular spaces can be represented by the functions:length: $f(x) = 3x$width: $g(x) = 2x$which function represents the area for any rectangular space in the building?$\bigcirc$ $6x^2LXB0\bigcirc$ $3x^2$$\bigcirc$ $10x$

Explanation:

Step1: Recall area formula for rectangle

The area of a rectangle is $\text{Area} = \text{Length} \times \text{Width}$.

Step2: Substitute given functions

Substitute $f(x)=3x$ (length) and $g(x)=2x$ (width):
$\text{Area} = f(x) \times g(x) = 3x \times 2x$

Step3: Simplify the product

Multiply coefficients and variables:
$3x \times 2x = (3 \times 2) \times (x \times x) = 6x^2$

Answer:

$6x^2$