Question 607220
The length of a rectangle is 4 inches longer than twice its width. The area of the rectangle is 96 square inches. What is the length and width of the rectangle?


Let x=length and y=width
{{{y-4=2x}}}
{{{xy=96}}}


Solve the first equation for y and substitute it into the 2nd equation
{{{y-4=2x}}}
{{{y=2x+4}}}


{{{xy=96}}}
{{{x(2x+4)=96}}}
{{{2x^2+4x=96}}}
{{{2x^2+4x-96=0}}}
{{{2(x^2+2x-48)}}}
{{{2(x+8)(x-6)=0}}}
{{{x=-8,6}}}
Reject x=-8 because the length cannot be a negative number
So x=6

Substitute x to find y
{{{y=2x+4}}}
{{{y=2(6)+4}}}
{{{y=12+4}}}
{{{y=16}}}