Question 1134826
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If you solve the problem using formal algebra, as in the solution by tutor @MathTherapy, you end up having to solve a quadratic equation by finding two numbers whose product is 1297, with one of the numbers 6 greater than the other.<br>
If instead of the formal algebra you solve informally, working directly with the given information, you have to find two numbers whose product is 2574 and whose difference is 12.  So you end up having to do the same kind of trial and error as with the formal algebra.<br>
So there is no advantage to using formal algebra.<br>
Tutor @addingup had the good idea to use this informal method for solving the problem; but he apparently overlooked the solution.<br>
The prime factorization of the given area is<br>
2574 = 2*2*3*11*13<br>
A little playing around with these prime factors will find two factors of 2574 that satisfy the given condition (one is 12 less than twice the other) are 39 and 66.<br>
So those are the dimensions of the rectangle; the length is 66m.