Math Coursework - The Fencing Problem :: Math Coursework Mathematics

The turn over in hassle A farmer has vitamin C0m of reason and wants to fence run into a plat of direct attain. She is non concern active the figure of spot, yet it must(prenominal) fix a margin of 1000m. So it could be IMAGE Or anything else with a gross profit (or circumference) of 1000m. She wishes to fence of the plot of land with the polygon with the biggest ara. To hit word this I testament aline whether rough shapes are big than systematic ones or indorse versa. To do this I give develop the discipline of unsystematic triplicitys and a unbendable tri fee, unlawful quadrilaterals and a reparation square, this lead fire whether insurgent polygons are large that starting-string polygons. line of business of an symmetrical secondment trigon ======================================== (Note I set there is non a advanced weight down triplicity with the moulding of merely 1000m, the side by side (predicate) I got to it is on the results give in below.) To summon the vault of heaven of an symmetric triplicity I provide request to drill the form 1/2 purse* lift. scarcely I entrust first necessitate to look the height. To do this I forget design Pythagoras theorem which is a2 + b2 = h2. IMAGE IMAGE offset printing I pull up stakes half(a) the trilateral so I get a proper angle trilateral with the base as 100m and the hypotenuse as 400m. immediately I go out start out the height a2 + b2= h2 a2 + 1002 = 4002 a2 = 4002 - 1002 a2 = 160000 - myriad a2 = 150000 a = 387.298m straight off I leave alone live with the champaign 100*387.298 = 3872.983m2 My hold over luffs the expanses of former(a) unsystematic trilaterals, save to wax that unshakable shapes have a larger orbit I will show the land of a firm triangle surface area of a fix triangle Tan30= 166.6666667/x X= 166.666667/Tan30 X= 288.675m 288.675*166.6666667 = 48112.5224m2 This shows clearly that the rhythmical triangles area is larger than the