Answer:
x(x +3) = 108
Explanation:
The longer string is 3 inches longer than the shorter string, whose length is x. Then the longer string is (x+3), and the product of their lengths is ...
x(x +3) = 108 . . . . . equation for finding the shorter length
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In standard form, the equation is ...
x² +3x -108 = 0
(x -9)(x +12) = 0 . . . . . factored form
The values of x that make these factors zero are 9 and -12. The shorter string length is 9 inches.
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Additional comments
John's guitar is unusually small if its strings are 12 inches or less.
Note that factoring is accomplished by finding factors of 108 that differ by 3. This requires the same thinking process as solving the problem directly without the use of an equation. We know the product of two numbers is 108 and one is 3 larger than the other.
The difference (3) is sufficiently smaller than the product that the square root of the product (10.4) will be about halfway between the numbers. We can reasonably guess their values to be 10.5±3/2 = {9, 12}. (There is a more formal way to make this calculation by defining a variable (a) to be the average of the two lengths: Then you have (a-3/2)(a+3/2)=108, or a² = 110.25 and a=10.5. This matches our approximation.)