Question 1200737
let the sides of the squar be equal to x.
if you take 5 cm off one side, then that side is equal to x - 5.
if you add 8 cm to the other side, then that side is equal to x + 8.
the resulting rectangle has two sides that are x - 5 and two sides that are x + 8.
the resulting permieter is equal to 2 * (x - 5) + 2 * (x + 8).
simplify to get  2x - 10 + 2x + 16
combine like terms to get 4x + 6
that is the perimeter.
since the perimeter is equal to 98, you get 4x + 6 = 98
subtract 6 from voth sides of the equation to get 4x = 92
solve for x to get x = 92/4 = 23.
the area of the original square is x^2 = 23^2 = 529 square cm.
the resulting rectangle is 23 - 5 by 23 + 8 = 18 by 31.
the diagonals form a right triangle with a height of 31 and a base of 18.
the diagonal is the hypotenuse of this right triangle.
the length of the diagonal is equal to sqrt(18^2 + 31^2) = sqrt(1285).
this is equal to 35.84689666