Denote by x the length of the side of the first square and by y the length
of the side of the second square.
We deduce from the figure the following equations:
[tex]x^2+y^2=116\text{ (The combined area)}\\2(x+y)=28\text{ (The perimeter)}\\\text{Solving the above system:}\\x=14-y\text{ then }(14-y)^2+y^2=116\\\text{Solving the above equation for y we get:}\\\text{ Either }y=4\text{ or }y=10.\\\text{The above values corresponds to}\\\text{ Either }x=14-4=10\text{ or }y=14-10=4.[/tex]
Answer: the length of the sides are 4 and 10.
