What is the reason aircraft are as long as they are wide?
By curious coincidence it is simply what the optimal aspect ratio for speeds around 250–280 knots indicated results in. Aircraft designed for different cruise speeds have different ratios.

The wing span is governed by desired cruise speed. There are two main forms of drag—induced and parasite. Induced drag decreases with wing span and with speed, while parasite drag increases with them. So at lower speed, you need long wings to keep the induced drag at bay, while parasite drag is low simply because of the low speed. And at higher speed, you need shorter wings to avoid too much parasite drag.

Jet aircraft are most efficient at transsonic speeds (Mach number 0.75–0.85) and altitudes around 10-12 km (33,000–40,000 ft) and it so happens that the wing span and cabin length to contain corresponding payload are similar. Turboprop aircraft are most efficient at somewhat lower speeds and altitudes and consequently their wings are a bit longer. And yet slower piston-powered aircraft have even longer wings relatively to fuselage.

(update, as suggested in comments): The extremes are on one side gliders that achieve low drag by having very long slender wings and flying slow and on the other side supersonic aircraft that have short wings with long chord to keep the frontal cross-section low, the very extreme being the very fastest aircraft like X-15 or SR-71.