Question

The length of a rectangular room is 12 feet more than 3 times the height of the room. The floor of the room has an area that is represented by the function below, where h is the height of the room in feet. A(R) 9h2 + 45h + 36 Which statement best describes the width of the room? A. The width is 3 feet shorter than the length. B. The width is 9 feet shorter than the length. C. The width is 9 feet longer than the height. D The width is 3 feet longer than the height.ill send a picture of the question

Answer 1

Okay, here we have this:

Considering the provided information, and that the area of a rectangle is the product of its length and width, we obtain the following:

`\begin{gathered} Width=(Area)/(Length) \\ Width=(9h^2+45h+36)/(3h+12) \\ =(9\left(h+1\right)\left(h+4\right))/(3h+12) \\ =(9\left(h+1\right)\left(h+4\right))/(3\left(h+4\right)) \\ =3\mleft(h+1\mright) \\ =3h+3 \end{gathered}`

Now, to know if the width is greater or less than the length, we will subtract it, then we have:

`\begin{gathered} (3h+12)-(3h+3) \\ =3h+12-3h-3 \\ =12-3 \\ =9 \end{gathered}`

Finally we obtain that the width is feet 9 shorter than the length, so the correct answer is the option B