Question

The area of a rectangular conference room is represented by the equation A = (x2 + 18x + 72) feet2. If x = 9 feet and the width = (x + 6) feet, what is the perimeter, in feet, of the room?


A.
315

B.
36

C.
72

D.
80

Answer 1

Answer:

72 ft  (answer C)

Step-by-step explanation:

Hello, Brittany,

You could find the length of the room by dividing the width (x+6) into the area (x^2 + 18x + 72) and then subbing 9 ft for x to obtain a final, numerical answer.  Or you could evaluate the area and width first, and then divide the area by the width.  Your choice.

(x^2 + 18x + 72) divided by (x + 6) is x + 12.  Note that 6*12 = 72 and that 6x + 12x = 18x, matching (x^2 + 18x + 72) perfectly.  The length is thus 9 + 12, or 21 ft.  

This gives us a perimeter P of 2L + 2W, or P = 2(21 ft) + 2(15 ft), or 72 ft.