Based on the given information, we can write the following equations:
#p=w+12#
#p=7w#
#p=2w+2l#
where #p# is the perimeter, #l# is the length, and #w# is the width.
Our goal is to find #l# in the third equation. But before we do this, we will need to solve for #p# and #w# in the first and second equations listed above (I am using the substitution method):
#p=w+12# and #p=7w#
#(color(blue)(p))=w+12#
#color(blue)((7w))=w+12#
#6w=12#
#color(red)(w=2)#
Now, we will use the width, #w=2#, to find the perimeter (it doesn't matter whether you use equation #1# or #2# here):
#p=7color(blue)(w)#
#p=7color(blue)((2))#
#color(red)(p=14)#
Now, we know both of the values of #p# and #w#, and we are ready to use them to find #l# using the third equation:
#color(green)(p)=2color(blue)(w)+2l#
#color(green)((14))=2(color(blue)(2))+2l#
#14=4+2l#
#10=2l#
#color(red)(l=5)#
Therefore, the length of your rectangle is #color(green)(5 " inches"#.
I hope that helps!
