He length of a rectangle is 7 in greater than the width. the area is 30 in squared2. find the length and the width

L=7+W

area=30=LW

so subsitute 7+W for length

30 = (7+W) (W)

30=W²+7W

minus 30 both sides

0=W²+7W-30

factor

what 2 numbers multiply to get - 30 and add to get 7

-3 and 10

0 = (W-3) (W+10)

set to zero

0=W-3

3=W

0=W+10

-10=W

false, can't have a negative width

width=3in

L=7+W

L=7+3

L=10

the length is 10in

the width is 3in