Let's look at what facts we are given.
The area is 35, which means LW=35.
We also know that width is two less than the length.
If we represent the length width X, then L=X-2. Using our area function X*L=35, we substitute our new value of L for X-2 and get X(X-2)=35. Distribute to get X2-2X=35 → set equal to zero by subracting 35 from both sides X2-2x-35=0.
With this polynomial, we find the factors. Two factors of 35 that have a digit difference of 2 are 5 and 7, but one has to be negative since 35 is negative in our polynomial and it must be the larger one because we have -2X instead of +2X in the middle. We get -7 and 5.
We can write our new factors as
(X-7)(X+5)=0, giving us critical values of 7 and -5. We aren't able to have negative lengths so our X value is 7. That's our Width. To find our Length we use L=X-2 → L=7-2 → L=5
There you have it, the Length is 5 cm and the width is 7 cm