Question 74859
Let the width = x cm. 
Two times width = 2x cm.
5cm more than this value = (2x + 5) cm
So, the length = (2x + 5) cm.


Hence area = Length X Width = {{{(2x + 5)x = 2x^2 + 5x}}} {{{cm^2}}}.


But, according to the problem this area is 75 {{{cm^2}}}.


So, {{{2x^2 + 5x = 75}}}
{{{2x^2 + 5x - 75 = 0}}}
{{{2x^2 + 15x - 10x - 75 = 0}}}
{{{x(2x + 15) - 5(2x + 15) = 0}}}
{{{(x-5)(2x+15)=0}}}


So either (x-5) = 0 or (2x+15) = 0
i.e. either x = 5 or x = -7.5


But width of a rectangle (x) cannot be negative.
So negative answer is discarded.
Hence x = 5.


So the width = 5 cm and length = 2x5 + 5 = 15 cm.