The length of a rectangle is 7 yd less than three times the width, and the area of the rectangle is 66 yd (squared). find the dimensions of the rectangle.

So legnt=l

width=w

l=-7+3w

l=3w-7

area=66

area=legnth times width or

area=lw

subisutte

area=lw

l=3w-7

66 = (3w-7) (w)

66=3w^2-7w

subtrac 66 from both sides

0=3w^2-7w-66

factor

HOW TO

multiply 3 and - 66=-198

find what 2 numbers add up to - 7 and multiply to get - 198

the numbers area 11 and - 18

so

3w^2-18w+11w-66=0

factor

(3w^2-18w) + (11w-66) = 0

(3w) (w-6) + (11) (w-6) = 0

factor using distributive (ab+ac=a (b+c))

(3w+11) (w-6) = 0

set them to zero

3w+11=0

subtract 11

3w=-11

legnths cannot be negative so we discard this

w-6=0

add 6

w=6

width=6

legnth=3w-7

length=3 (6) - 7

legnt=18-7

legnth=11

width=6

legnth=11