an engineer is designing a building and wants rectangular spaces to maintain a ratio of 2 to 3. for any…

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? 6x² 6x 3x² 10x

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? 6x² 6x 3x² 10x

Answer

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = \text{length}\times\text{width}$.

Step2: Substitute given functions

We are given length $f(x)=3x$ and width $g(x) = 2x$. So $A(x)=f(x)\times g(x)=(3x)\times(2x)$.

Step3: Simplify the expression

Using the rule of exponents $a^m\times a^n=a^{m + n}$ and multiplying the coefficients, $(3x)\times(2x)=(3\times2)\times(x\times x)=6x^{2}$.

Answer:

$6x^{2}$