Question 125035
x = width
3x = length

Area = Length X Width, so {{{A=3x*x=3x^2}}}


{{{3x^2=75}}}


{{{x^2=25}}}


{{{red(x^2-25=0)}}}, which is your quadratic equation in standard form.



Factors to:


{{{(x+5)(x-5)=0}}}


So, {{{x=-5}}} or {{{x=5}}}.  The negative result doesn't make much sense in terms of the dimensions of a rectangle, so we can exclude that root.  The width of the rectangle is therefore 5 meters, and the length is 3 * 5 =15 meters.