Question 59607
Let l be the length , w be the width and h be the height of the room.
Then l + w + h = 42--------------(1)
Also given l + h = 2w
Plugging in this value in (1) ,
w + 2w = 42
==> 3w = 42
==> 3w/3 = 42/3
==> w = 14
So width = 14 ft

Area of the floor = 280 sq ft
==> l*w = 280
==> l*14 = 280
==> 14 l = 280
==> 14 l/14 = 280/14
==> l = 20
So length = 20 ft

Plugging in the values of l and w in (1) we get
20 + 14 + h = 42
==> 34 + h = 42
==> h = 42 - 34
==> h = 8
So height = 8 ft

The dimensions are 20 ft, 14ft and 8ft.

Good Luck!!!