The gilbert's are designing a rectangular patio. the patio has an area of 432 square feet. the width of the patio is 3/4 it's length. what is the length of the patio?

Area=legnth times width
a=lw
area=432

width is 3/4 its lenth
w=3/4 times l
subsitute
a=l(3/4 times l)
a=432
432=l(3/4 times l)
432=3/4l^2
multiply both sides by 4/3 to clear fraction
1728/3=l^2
576=l^2
take the squaer root of both sides
24=l
subsitute
w=3/4l
w=3/4(24)
w=18

legnth=24 feet
width=18 feet