Work the area of a rectangle out but already knowing the area and needing to know the length as it is two centermeters more than the width, area being 469

The area of a rectangle is the length times width:

a = l*w

the length is 2 centimeters more than the width:

l = w + 2

express area in terms of width

a = l*w

a = (w + 2) w

a = w^2 + 2w

w^2 + 2w = 469

w^2 + 2w - 469 = 0

we can solve using the general quadratic formula:

w = (-2 + - √ (4 + 1876)) / 2

w = (-2 + - 43.36) / 2

we use the positive solution:

w = (-2 + 43.36) / 2

w = 20.68

thus the width is 20.68 cm

l = w + 2 = 20.68 + 2

l = 22.68

and the length is 22.68 cm