Question

The room and the hallway shown in the floor plan below have different dimension but the same area. Find value of w.

Answer 1

w=9

The room has dimensions of w w+3 so its area is w(w+3)=
`w^(2)+ 3w`

The hallway has dimensions of w−3 so its area is 2w(w−3) =
`2w^(2) - 6w`

If the room and hallway have the same area, then

`w^(2)+ 3w = 2w^(2) - 6w`

`w^(2) - 9w = 0`

w(w-9) = 0 , Factors

Since w is a dimension of the room, then w>0 so w=0 cannot be the value of w. Therefore w=9

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Answer 2

check the picture below

if their areas are equal then A =A or
(3w)(w-2) = (w+1)(w)

solve for "w"