684.76 ft. (for 600), 456.51 ft. (for 400), and 228.25 ft. (for 200). The least amount of wire needed would be 684.75 ft for 3 wires at a 200 foot height.
Work Step by Step
The equation you could use to model this would be the square root of h squared + 0.55h squared. Using the formula given, we can plug in each height, h, given on the diagram. For a height of 600 feet, we set h=600, then plug it in = 684.76 feet. For a height of 400 feet, we set h=400, then plug it in = 456.508 feet. For a height of 200 feet, we set h=200, then plug it in= 228.254 feet. According to our above calculations, in order to use the least amount of wire, we would want to use the 200-foot height. Since we just calculated that each wire would be about 228.25 ft long, we will multiply that by 3 wires to obtain how much wire we need for all 3 wires. 228.25 * 3 = 684.75 feet of wire.