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Ratio of two corresponding sides of the similar kites = 3/8

Step-by-step explanation:

A kite has two pairs of congruent consecutive sides

Perimeter of a kite, P = 2(a + b)

Let the sides of the first kite be a and b; and the side of the second kite be e and f

Kite ABCD:

24 = 2(a + b)

12 = a + b

a = 12 - b

Kite EFGH

64 = 2(e + f)

32 = e + f

e = 32 - f

For a kite to be similar, the ratio of the side must be the same.

Considering a to correspond to e and b to correspond to f, therefore:

b/f = 12 - b/32 - f

32b - bf = 12f - bf

32b = 12f

b/f = 12/32

b/f = 3/8