The area of a rectangular shaped cake is 507 cm2 .

The length of the cake is three times bigger than the width? What is the length and width of the cake?

width === x

length is 3 times bigger ==== > length = 3x

area = length * width
507 = x(x+3)

expand, re-write in standard quadratic notation, then solve
using your favorite method to solve quadratics.