The golden ratio is equal to 1.618. This means that the ratio between the two sides of the bed must be equal to that value. We were given the shorter side of the bed, therefore to find the length of the longer side we need to multiply the short one by the golden ratio.
[tex]\text{longer = 1.618}\cdot4=6.472\text{ ft}[/tex]The longer side will be approximately 6.5 ft