Square 1 has a side length of x, and square 2 has a side length of y. Square 2 is formed by joining the midpoints of the sides of square 1 in order. If x = 2, find the ratio of the perimeter of square 1 to the perimeter of square 2.

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By the Pythagorean Theorem, side y will be equal to the square root of the sum of the sides x/2 squared... because the sides of the smaller square will have sides of x/2... y=√[(x/2)^2+(x/2)^2] y=√(2(x/2)^2) y=√((x^2)/2) y=x/√2 The perimeter of the larger square will be 4x and the perimeter of the smaller square will be 4y=4x/√2 the ratio of the smaller to the larger will be: 4x/√2:4x  since x=2 8/√2:8 1/√2:1 √2/2:1 √2:2 2:2√2 1:√2

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