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