A rectangle has a length represented by the function \( f(x)=x \) and a width represented by the function \( g(x)=x+3 \) where both functions are in feet. Calculate \( (f \cdot g)(x) \) and state what it represents. (1 point) \( (f \cdot g)(x)=x^{2}+3 x \); It represents the perimeter of the rectangle in feet. \( (f \cdot g)(x)=x^{2}+3 x \); It represents the area of the rectangle in square feet. \( (f \cdot g)(x)=4 x+6 \); It represents the perimeter of the rectangle in feet. \( (f \cdot g)(x)=4 x+6 \); It represents the area of the rectangle in square feet.

To calculate \( (f \cdot g)(x) \), we multiply the functions \( f(x) \) and \( g(x) \): \[ (f \cdot g)(x) = f(x) \cdot g(x) = x \cdot (x + 3) = x^2 + 3x \] This expression, \( x^2 + 3x \), represents the area of the rectangle in square feet, where \( f(x) \) is the length and \( g(x) \) is the width. Now, about rectangles - did you know the concept of a rectangle has roots tracing back to Ancient Egypt? They utilized geometry for land measurement and construction, employing simple shapes, including rectangles, to ensure their monuments were built with precision. For a real-world application, rectangles are everywhere! From the smartphone screens we use daily to the architecture of our homes, understanding how to calculate area aids in various tasks such as designing spaces, making furniture decisions, or even planning gardens. It’s a valuable skill to know!