The length of a rectangle is 1cm more than three times the width if the area of the rectangle is 30cm^2 ,how many centimeters is the width?

3 cm

Step-by-step explanation:

if width is x, length is 3x+1

area = length * width

30 = x * 3x+1

30 = 3x^2 + x

0 = 3x^2 + x - 30

factor to get:

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

set both sides equal to zero

-10 = 3x  --> no solution because you can't have a negative width

3=x --> the width is 3 cm