Problema Solution
a rectangular room is 4 meters wider than it is high and it is 8 meters longer than it is wide. The total area of the walls is 512 square meters. Find the width of the room
Answer provided by our tutors
The width is 4 meters greater than the height, so:
w = h + 4
The length is 8 meters greater than the width:
l = w + 8
The total area of the four walls is 512 square meters:
512 = 2lh +2wh = 2h (w+l)
We have three equations, and three unknowns.
l = (h+4) + 8 = h + 12
512 = 2h ((h+4)+(h + 12))
512 = 2h (2h + 16) = 4h^2 + 32 h
16 = 1/8 h^2 + h
h = 8
w = h + 4 = 12
The width of the room is 12 meters.