1. Since a square can be divided into 2 right triangles the length of the diagonal can be calculated using the pythagorean theorem.

a^2+b^2=c^2

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

a^2+a^2=(a+5)^2

2a^2=a^2+10a+25

a^2=10a+25

Which can be further rearranged to make a quadratic function

a^2-10a-25=0

Which unfortunately cannot be factored so we have to use the quadratic formula

x=[-bħsqrt(b^2-4ac)]/2a

x=[10ħsqrt([-10]^2-4[1][-25])]/2(1)

x=[10ħsqrt(100+100)]/2

x=[10ħsqrt(200)]/2

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.