Question 1125767
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From the condition, we have these two equations


m + n = 9,                (counting the sides)

{{{(m*(m-3))/2}}} + {{{(n*(n-3))/2}}} = 7    (counting the diagonals).



Equivalently

m + n = 9,                

{{{m*(m-3)}}} + {{{n*(n-3)}}} = 14.



Equivalently

m + n = 9,                

{{{m^2-3m}}} + {{{n^2-3n}}} = 14.
    


Equivalently

m + n = 9,                

{{{m^2}}} + {{{n^2}}} = 14 + 3*(m+n) = 14 + 3*9 = 14 +27 = 41.



Thus you have these two equations

m + n = 9,         (1)

m^2 + n^2 = 41.    (2)



From (1), express m = 9-n  and substitute it into (2).
You will get a quadratic equation. Solve it by any way you want.



<U>Answer</U>.  4 sides and 5 sides.
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