How do you answer this?

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1 Answer
Feb 11, 2018

The length is #4# times longer than the width

#W:L# :: #1:4#

Explanation:

#(1)# When the longer sides are touching, the perimeter is
"the sum of two lengths plus four widths"
2L + 4W

#(2)# When the shorter sides are touching, the perimeter is
"the sum of four lengths plus two widths"
4L + 2W

#(3)# 4L + 2W is #50%# larger than 2L + 4W

"#50%# larger" can be expressed as "#1.5# times larger"
#1.5# (2L + 4W) = 4L + 2W

#4)# Clear the parentheses by distributing the #1.5#
3L + 6W = 4L + 2W

#5)# Subtract 3L from both sides
6W = L + 2W

#6)# Subtract 2W from both sides to isolate L
4W = L

This result means that L is four times longer than W.
It takes four widths to equal one length.

#"Answer"#
#W:L#  ::  #1:4#

Check

Let width equal #1#

When the longer sides are touching, the perimeter is
#4 L  + 2 W =  P#
#4(1) + 2(4) = 12#

When the shorter sides are touching, the perimeter is
#2 L + 4 W = P#
#2(1) + 4(4) = 18#

#18 = 50% "more than"  12#

#Check#