The perimeter of a rectangular wooden deck is 90 feet. The deck's length, I, is 5 feet less than 4 times its width, w. Which System of linear equations can be used to determine the dimensions, n feet, of the wooden deck?

Question

Savannah Anderson · Accepted Answer

#"length"=35 " feet"# and #"width"=10" feet"# You are given the perimeter of the rectangular deck is #90# feet. #color(blue)(2xx"length"+2xx"width"=90)# You are also given that the deck's length is #5# feet less than #4# times it's width. That is #color(red)("length" = 4xx"width"-5)# Those two equations are your system of linear equations. The second equation can be plugged into the first equation. This gives us an equation entirely in terms of #"width"#. #color(blue)(2xx(color(red)(4xx"width"-5))+2xx"width"=90)# Distribute the #2# through #8xx"width"-10+2xx"width"=90# Combine your term's with #"width"# #10xx"width"-10=90# Add #10# to both sides. #10xx"width"=100# Divide both sides by #10# #color(green)("width"=10)# Now you can plug #"width"# into your original equation for length above. Recall: #color(red)("length" = 4xx"width"-5)# #color(red)("length" = 4xxcolor(green)(10)-5)# #"length"=40-5# #"length"=35# ANSWER: #"length"=35 " feet"# and #"width"=10" feet"#

Jace Anderson · Answer

undefined The system of linear equations that can be used to determine the dimensions, in feet, of the wooden deck is:

1. $2w + 2l = 90$
2. $l = 4w - 5$