Area of 320 square feet, the width of the room is 4/5 it's length

Area=legnth times width or

a=lw

if w=4/5l

and a=320 then subsitute 320 for a dn 4/5l for w

320=4/5l times l

multiply both sides by 5 to clear fraction

1600=4l times l

ad like terms

1600=4l^2

subtract 1600 from both sides

0=4l^2-1600

try and factor because if you have xy=0 then x and/or y=0 so

difference of 2 perfect squares where

if you have a^2-b^2 then that equals (a-b) (a+b) so

0 = (2l) ^2 - (40) ^2 = (2l-40) (2l+40)

so 2l-40=0

add 40 to both sides

2l=40

divide by 2

l=20

if

2l+40=0

subtract 40 from both sides

2l=-40

divide 2

l=-20

since meausrements of real objects cannot be negative, wediscard this number

l=20 is thhe true legnth s

subsitute

w=4/5l

w=4/5 (20)

w=80/5

w=16

legnth=20

width=16