let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

A = 116 cm^2 the area of the rectangle

the width of a rectangle is 2 less than twice its length

w = 2l - 2

the are of the rectangle is 116 cm^2

l*w = 116

plug w = 2l - 2 into the above equation

l*(2l - 2) = 116

by solving we find

l = (1/2)(1 + √233)

click here to see the step by step solution of the equation

w = 2*(1/2)(1 + √233) - 2

w = -1 + √233

using the Pythagorean Theorem we find the diagonal d

d^2 = l^2 + w^2

d^2 = (1/2)(1 + √233)^2 + (-1 + √233)^2

d = 4.73 cm approximately

click here to see the step by step calculation

the diagonal is 4.73 cm approximately long.