Let x be the number (now unknown) which is exactly half way between the width and the length of the playground.


Then, as you understand,  the length = (x+1)  and  the width = (x-1).


The area = 168 = length*width = (x+1)*(x-1).


Thus (x+1)*(x-1) = 168,  which implies   = 168,  i.e.   = 168+1 = 169.


Hence, x =  = 13.


Then the length = 13+1 = 14  and the width = 13-1 = 12.

The method above you may find in some recreational books.

Sometimes in math circles the teachers explain it to students.


But in the school Math, the standard method of solution is to reduce the problem to a quadratic equation

w*(w+2) = 168

and then solve it using the quadratic formula or factoring.


When you do it by factoring, you need to guess two numbers with the difference of 2 and the product of 168.


You can do it by sorting through different factors of the number 168, as the tutor @shin123 explained it in his post.