Question

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

Answer 1

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