# Sum of the areas

Let the side of the large square and small square be x cm and y cm respectively.

According to the question,

x2+y2 = 400...(1)

and,

4(x-y) = 16

x-y = 4

x = y+4 ...(2)

Substituting the value of x in equation (1), we get-

(y+4)2+y2 = 400

2y2+8y+16 = 400

2y2+8y-384 = 0

y2+4y-192 = 0

y2+16y-12y-192 = 0

y(y+16)-12(y+16) = 0

(y-12)(y+16) = 0

(y-12) = 0 or (y+16) = 0

y = 12 or y = -16

the value of y = -16 is invalid because the length of the side can't be negative.

Thus, Side of small square = y = 12 cm

and Side of large square = x = 4 + y [from (2)]

= 16 cm

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