The diagonal of a rectangle exceeds the length by 2 cm. If the width of the rectangle is 10cm. find the length using pythagorean theorem answer according to book is 24 cm and my work got me 9.79 (10^2+b^2=2^2)
what exceeds means exactly here? what is the original value of the diagonal?

Exceeds means is longer than.  If the length is $b$ cm then the diagonal is $2$ cm longer; so the diagonal is $b +2$.
In a rectangle if the width is $a$ and the length is $b$ and the diagonal is $c$ you have the formula $a^2 + b^2 = c^2$.
In this case we have the width is $10$ and we dont know what the length is (so we'll call it $b$) and the diagonal is $b+2$.
So we  have $10^2 + b^2 = (b+2)^2$.
Solve for $b$.
Then the length will be $b$ 
And the diagonal will be $b + 2$.
