Question 404866
if the width of the rectangle is x inches, then the length is (x+7)
The area of the rectangle is {{{S=W*L}}}, W- width, L-length
So the area is {{{x*(x+7)}}}
Equation
{{{x*(x+7)=98}}}
{{{x^2+7x-98=0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-7 +- sqrt( 7^2-4*1*(-98) ))/(2*1) }}}
{{{x = (-7 +21)/2=7 }}}  or {{{x = (-7 -21)/2=-14<0 }}}Extraneous root of the equation
The width is 7 inches, then the length is {{{7+7=14}}} inches
Answer 7 inches and 14 inches