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A museum has one large square gallery. The director wants to subdivide this room down the middle into four smaller square rooms.(a) What will be the increase in wall area?
Ans. k1 for one square = 88.62%; k2 for 4 squares is 88.62/2 = 44.31%. From Eq. 3, new perimeter p2 ÷ p1 = k1÷ k2 = 2. The wall space will be doubled.(b) Suppose the director decided to divide the square room lengthwise into four narrow rooms, each with a length-to-width ratio of 4:1. What would be the increase in wall area?From Eq 4b, k for one room is 70.898% and from Eq. 2, k is 35.45% for the four rooms. Thus from Eq. 3, the increase in wall area is .8862/.3545 = 2.5. The new gallery wall space will be 2.5 times the original wall space.
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