Answer:
12 meters
Step-by-step explanation:
Let w represent the width of the room in meters. Then the height is w-4, and the length is w+8.
The wall area is the product of the height and the perimeter. The perimeter is twice the sum of length and width.
A = hP
P = 2(l+w) = 2(w+8 +w) = 4w+16
A = (w -4)(4w +16) = 4(w² -16)
The area is 512 square meters, so we have ...
512 = 4(w² -16)
128 = w² -16 . . . . . . divide by 4
144 = w² . . . . . . . . add 16
12 = w . . . . . . . . . take the square root
The width of the room is 12 meters.
