Question 1184836
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Let x be the side of the larger square and y be the side of the smaller square.  Then<br>
The area of the larger is 55 more than the area of the smaller:
x^2-y^2=55<br>
The perimeter of the larger is 8 more than the perimeter of the smaller (so the side of the larger is 2 more than the side of the smaller):
x=y+2<br>
With that pair of equations, you clearly want to use substitution.<br>
(y+2)^2-y^2=55<br>
That is easily solved for y; then x is y+2.<br>
I leave it to you to finish the calculations.<br>