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?

Answer 1

In any rectangle, the area is given by the product of the width and the length.

Since in this case both dimensions are represented by the correspondent function, you need to multiply the function:

`A(x) = f(x)\cdot g(x) = 3x \cdot 2x = 6x^2`

Answer 2

Area = 6x²

Explanation:

Rectangle space of the building is in the ratio of 2: 3

For any measurement value x, length of the rectangular space is represented by f(x) = 3x

and width is represented by g(x) = 2x

As we know area of any rectangle is measured by (Length × width)

Area = f(x) × g(x)

= (3x)(2x)

= 6x²

Therefore, area of the rectangle will be represented by Area = 6x²