A rancher wants to fence in an area of 3,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
Accepted Solution
A:
Answer:shortest length of fence is 8485.2 ftStep-by-step explanation:Given dataarea = 3,000,000 square feetto find out shortest length of fence let length L and width is Wso area is L × WW = 3 × [tex]10^{6}[/tex] /L ............12W = 6 × [tex]10^{6}[/tex] /Lrectangular field and then divide it in half so fencing will be 3 × L + 2 × Wi.e. 3 L + 2Wfencing = 3 L + 6 × [tex]10^{6}[/tex] /Lfencing minimum = 3 L - 6 × [tex]10^{6}[/tex] /L² fencing minimum length will be zero3 L - 6 × [tex]10^{6}[/tex] /L² = 03 L² = 6 × [tex]10^{6}[/tex]L² = 2 × [tex]10^{6}[/tex]L = 1414.2so from equation 1 W = 3 × [tex]10^{6}[/tex] /LW = 3 × [tex]10^{6}[/tex] /1414.2W = 2121.3so fencing will be 3 L +2 Wso fencing = 3 × 1414.2 +2 × 2121.3fencing = 4242.6 +4242.6fencing = 8485.2shortest length of fence is 8485.2 ft