Sometimes when you're given dimensions that differ by some amount, it is easier to work with their average value. Let x represent the average of length and width of the rectangle. The length and width differ from this average value by 1.5 m. Then the area is
.. (x +1.5)*(x -1.5) = 154
.. x^2 -2.25 = 154
.. x^2 = 156.25
.. x = 12.5
The width is 1.5 m shorter than this, or 11 m.
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Solved in the conventional way, you are looking for factors of 154 that differ by 3. This means you have to find the factors of 154, or use the quadratic formula.
.. 154 = 1*154 = 2*77 = 7*22 = 11*14 (the pair we want)
Once you have the factorization of 154, you have the answer. No equations are necessary, really.
