Question 223710
What is the length of a rectangle is twice its width if the width is increased by one meter and the length is diminished by three meters the area will be 12 square meters.


Step 1.  Let w be the width


Step 2.  Let 2w be the length.


Step 3.  Let w+1 be the width increased by one meter.


Step 4.  Let 2w-3 be the length diminished by three meters.


Step 5.  The Area A=(w+1)(2w-3)=12 since the area will be 12 meters with these changed dimensions.


Step 6.  Solving the equation in Step 5 will lead to a quadratic equation as follows:


{{{2w^2-3w+2w-3=12}}}


Subtract 12 from both sides of the equation


{{{2w^2-w-3-12=12-12}}}


{{{2w^2-w-15=0}}}


Step 7.  To solve, use the quadratic formula given as {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


where a=2, b=-1, and c=-15.


*[invoke quadratic "x", 2, -1, -15 ]


Selecting the positive solution given as {{{w=3}}}, then {{{2w=6}}}.  Check area A with width 3+1=4 and length 2w-3=3.  So the area with these dimensions is 12 as given by the problem statement.


Step 8.  ANSWER:  The length is 6 meters.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J