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The midpoints of the adjacent sides of a square are connected to form a new square. What is the number of inches in the perimeter of the new square if the perimeter of the original square is 16 inches

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mathstudent55

Answer:

8√2 in.

Step-by-step explanation:

The original square:

Perimeter = 16 in.

Side = 4 in.

New square:

Each side of the new square is the hypotenuse of an isosceles right triangle with legs of length 2 inches.

(2 in)² + (2 in.)² = s²

s² = √(8 in.²)

s = 2√2 in.

p = 4s = 4(2√2) in. = 8√2 in.