What is the length of the diagonal of the smaller square is equal to the width of the larger square

Drawing the diagonal will give you two right triangles. The right triangle will have two sides both equal to 10. Ti find the hypotenuse (the diagonal) use the pythagorean theorem a^2 + b^2 = c^2 where a=b=10
therefore 
10^2 + 10^2 = c^2
100 + 100 = c^2
200 = c^2
take the square root of both sides to find c
square root of 200 = (square root 2)(square root 100) = c
therefore 10(square root 2) = c
or
you can use a calculator to compute square root (200)

14.142 = c