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eimsori [14]
2 years ago
7

A square region with perimeter 60 inches is made with square inch tiles. Bob removes one tile from the square and rearranges the

remaining tiles without any overlap to make a rectangular region with minimum perimeter. How many inches are in the perimeter
Mathematics
1 answer:
icang [17]2 years ago
3 0

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.

<h3>Rectangle dimensions</h3>

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

<h3>Perimeter</h3>

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.

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