Question 1053332
w and L
L=3w
Original area is wL.


Dimensions changes this way:
L-2 and w+3.
New area is  (w+3)(L-2).


New area rectangle is 42.
{{{system((w+3)(L-2)=42,L=3w)}}}
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Use algebraic or arithmetic steps to solve from that.



STEPS TO BEGIN:
{{{(w+3)(3w-2)-42=0}}}
{{{3w^2+7w-6-42=0}}}
{{{3w^2+7w-48=0}}}
Look for a factorization, but immediately using formula for general solution of quadratic equation,
{{{w=(-7+- 25)/6}}}, and need the PLUS form;
{{{w=18/6}}}
{{{highlight(w=3)}}}


You can finish the work to finally answer the question.





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discriminant,  {{{49+4*3*48=49+12*48=625=25^2}}}