1. Since a square can be divided into 2 right triangles the length of the diagonal can be calculated using the pythagorean theorem.
c is the hypotenuse, the diagonal of the square.
Since we know that the hypotenuse is 5 inches longer than a side of the square (and all sides are equal) we can use the equation
Which can be further rearranged to make a quadratic function
Which unfortunately cannot be factored so we have to use the quadratic formula
x=10+sqrt(200)/2 or x=10-sqrt(200)/2
since sqrt(200) is approximately 14 and a length cannot be negative
x=10+sqrt(200)/2 <--exact answer
x=12.0710678 <--rounded answer
So side length of the square is 12.0710678 inches and the length of the diagonal is 17.0710678
Please keep in mind I haven't done this type of problem for a month or two and may have made a mistake somewhere, but that is the general idea of how to do it.