Question 141626
If the width is x, then the length must be x + 1 because the dimensions are consectutive integers.  The given area is 90, so {{{x(x+1)=90}}}


{{{x(x+1)=90}}}


{{{x^2+x-90=0}}}


Solve the quadratic excluding the extraneous negative root to get the width, add 1 to get the length, and then use the Pythagorean Theorem to calculate the length of the diagonal.  You should probably leave your answer in terms of a radical, but if you do choose to express the numerical approximation, it should be rounded to the nearest centimeter.  That's because your least precise given measurement -- the area -- was given to the nearest square centimeter.