Q. 225.0( 8 Votes )

Sum of the areas

Answer :

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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