Answer:
60 inches
Step-by-step explanation:
The perimeter will be minimized when the tiles are rearranged to form a rectangle with dimensions as close to each other as possible.
The square has a side length of ...
P = 4s ⇒ s = P/4 . . . . . P is perimeter, s is side length
(60 in)/4 = 15 in . . . . length of the side of the square
The square has an area of ...
A = s²
A = (15 in)² = 225 in²
When 1 tile is removed, the resulting area, in square inches, is ...
A = 225 -1 = 15² -1² = (15 -1)(15 +1) = 14×16
The perimeter of a rectangle is given by ...
P = 2(L+W)
For this rectangle, the perimeter is ...
P = 2(14 in + 16 in) = 2(30 in) = 60 in
The perimeter of the rectangle is 60 inches.
