Question 171289
If the original dimensions are 15 by 18 and they are both reduced by the same amount, then the new dimensions are {{{x}}} and {{{x + 3}}}.  The original area was 15 times 18 or 270 square centimeters.  116 square centimeters less than 270 is 154 square centimeters which is the area of the new rectangle.


So:

{{{x(x+3)=154}}}


{{{x^2+3x-154=0}}}


Since {{{-11*14=-154}}} and {{{-11+14=3}}}, the quadratic factors to:


{{{(x-11)(x+14)=0}}}, so


{{{x=11}}} or {{{x=-14}}}


-14 is absurd because you can't have a negative dimension, so exclude this root as extraneous.  That means that the new width of the rectangle is 11, and the new length is 3 more than that or 14.


Check:  11 * 14 = 154, 154 + 116 = 270, 15 - 4 = 11, and 18 - 4 = 14.  So all the original problem parameters are satisfied.  Answer checks.