The rooms dimensions

Question

The length of a rectangular room is 7 feet longer than twice the width. If the room's perimeter is 158 feet, what are the rooms dimensions?

Answer 1

Let w represent the width (in feet) of the room. Twice the width is 2w, so the length is 7 + 2w. The perimeter of a rectangle is twice the sum of length and width. Thus 

 

158 = 2[(7 + 2w) + w]

 

158 = 2(7 + 3w)

 

Divide both sides by 2 to get

 

79 = 7 + 3w 

 

Now subtract 7 from both sides.

 

72 = 3w

 

Finally, divide both sides by 3.

 

24 = w

 

Therefore, the width is 24 feet and the length is 7 + 2(24) = 55 feet. Consequently, the dimensions of the room are 24 ft × 55ft.