The formula for the perimeter of a rectangle is:
#p = 2(l + w)#
Let's call the width: #w#
Then, we can write the length as: #l = 2w + 8"m"#
We know the perimeter is #94"m"#.
We can substitute and solve for #w# as:
#94"m" = 2(2w + 8"m" + w)#
#94"m" = 2(2w + w + 8"m")#
#94"m" = 2(3w + 8"m")#
#94"m" = 6w + 16"m"#
#94"m" - color(red)(16"m") = 6w + 16"m" - color(red)(16"m")#
#78"m" = 6w + 0#
#78"m" = 6w#
#(78"m")/color(red)(6) = (6w)/color(red)(6)#
#13"m" = (color(red)(cancel(color(black)(6)))w)/cancel(color(red)(6))#
#13"m" = w#
#w = 13"m"#
Then we can calculate the #l# substituting:
#l = 2w + 8"m"# becomes:
#l = (2 xx 13"m") + 8"m"#
#l = 26"m" + 8"m"#
#l = 34"m"#
The Solution Is: #w = 13"m"# and #l = 34"m"#
#p = 2(13"m" + 34"m")#
#p = 2(47"m")#
#p = 94"m"#
