Question 824982
The length of a rectangle is 3 times it's width. If both dimensions are increased by 2 centimeters, the area is 32 square centimeters. What was the original length?



Width = x
Length = 3x


"If both dimensions are increased by 2 centimeters, the area is 32 square centimeters" ---> {{{(x+2)(3x+2)=32}}}


{{{(x+2)(3x+2)=32}}}


{{{x(3x+2)+2(3x+2)=32}}}


{{{3x^2+2x+6x+4=32}}}


{{{3x^2+2x+6x+4-32=0}}}


{{{3x^2+8x-28=0}}}


{{{(x-2)(3x+14)=0}}}


{{{x-2=0}}} or {{{3x+14=0}}}


{{{x=2}}} or {{{3x=-14}}}


{{{x=2}}} or {{{x=-14/3}}}


Toss the negative solution. So the only solution is {{{x=2}}}


Width = x = 2


Length = 3x = 3*2 = 6


The width is 2 centimeters and the length is 6 centimeters