The length of a rectangle is 7 cm than 6 times its width. It's area is 10 square centimeters. Find the dimensions

So legnth is 7 more than 6 times width

l=7+6w

area=10 cm^2

lw=area

subsitute

7+6w for l

(7+6w) (w) = 10

7w+6w^2=10

subtract 10 from both sides

6w^2+7w-10=0

factor

multiply 6 and - 10

get - 60

now find what 2 numbers multiply to get - 60 and add to get 7

the answe ris - 5 and 12

split up 7w into that

6w^2+7w-10=0

6w^2+12w-5w-10=0

group

(6w^2+12w) + (-5w-10) = 0

undistribute factors

(6w) (w+2) + (-5) (w+2) = 0

reverse distribute (ab+ac=a (b+c)

(w+2) ((6w) + (-5)) = 0

(w+2) (6w-5) = 0

set each to zero

w+2=0

subtract 2

w=-2

false, legnths cannot be negative

6w-5=0

add 5

6w=5

divide both sides by 6

w=5/6

subsitute

l=7+6w

l=7+6 (5/6)

l=7+5

l=12

legnth=12 cm

width=5/6 cm