Question 151040
Area of Rectangle =Length(L) X Width(W) or A=LW

In this case, let L=AB=4n+1 and let W=AD=n-5, so our equation to solve is:

(4n+1)(n-5)=25 ; Expand using FOIL
4n^2-20n+n-5=25 subtract 25 from each side and collect like terms
4n^2-19n-30=0  quadratic in standard form. Solve using the quadratic formula
{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{n = (19 +- sqrt( (-19)^2+4*4*30 ))/(2*4) }}} 
{{{n= (19 +- sqrt( 361+480 ))/(8) }}} 
{{{n = (19 +- 29)/8}}} 
n=(19+29)/8=48/8=6 
and
x=(19-29)/8=-10/8

CK for n=6 
AB=4n+1=4*6+1=25 cm-------------------------AB
AD=n-5=6-5=1 cm----------------------------------AD
and AB*AD=25*1=25  good!

CK for n=-10/8 
4n+1=4*(-10/8)+1=-5+1=-4 cm-----------No good!! Lengths in this case are positive

Hope this helps---ptaylor