Let the width be w, then the length is w+4 (in).
The area of the rectangle is [tex]A=w(w+4)= w^{2}+4w [/tex].
The perimeter of the rectangle is:
P = 2(Width + Length)=2(w+w+4)=2(2w+4)=4w+8
"The area of the rectangle is equal to 4 inches less than 5 times the perimeter." means that:
A = 5P - 4
[tex]w^{2}+4w=5(4w+8)-4[/tex]
[tex]w^{2}+4w=20w+40-4[/tex]
[tex]w^{2}-16w-36=0[/tex]
add and subtract 64 to complete the square:
[tex]w^{2}-16w+64-64-36=0[/tex]
[tex](w^{2}-16w+64)=100[/tex]
[tex](w-8)^{2}=10^{2} [/tex]
thus w= 18 or w=-2, but the width clearly cannot be negative.
w=18, the length is 18+4 = 22 (in)
Answer:
w=18 in, l=22 in
