Question

A rectangular room is 4 metres wider than it is High and it is 8 metres longer than it is wide. The total area of the walls is 512 square metres. Find the width of the room.​

Answer 1

12 meters

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.