SOLUTION: The floor of the recreation room in a house is a rectangle. The sum of its length, width, and height is 42 feet. The sum of its length and height is double its width. The area o

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Question 59607: The floor of the recreation room in a house is a rectangle. The sum of its length, width, and height is 42 feet. The sum of its length and height is double its width. The area of its floor is 280 square feet. What are the dimensions of the recreation room?
Answer by uma(370) About Me  (Show Source):
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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!!!