Set up appropriate systems of two linear equations in two unknowns and then solve the systems by determinants. All numbers are accurate to at least two significant digits.

Since ancient times, a rectangle for which the length L is approximately 1.62 times the width w has been considered the most pleasing to view, and is called a golden rectangle. If a painting in the shape of a golden rectangle has a perimeter of 4.20 m, find the dimensions.