]]> You and Lester decide to go into business building llama pens, since you had such great results with Latisha's pen. You want to create some general building guidelines to help in your business, and need to know:
Given any length of fence, what proportion of height to width will create a pen with the largest possible area?
Experiment with the next three pages and come back to this page with the ideal height/width ratio for a 36, 25, and 50 meter length of fence. Write your building guidelines for any length of fence in the pad. ]]>

]]> What is the ideal ratio of height to width for 36 meters of fencing?
Use the red dot to change the amount of fencing used for height versus width. Click the Sample button to measure the height, width, and area for this pen shape. Click the Clear button to erase all of your measurements.
When you're done, go back to page 1 to record your ratio. ]]> {1} Point(207,144)[hidden]; {2} Point(36,144)[hidden]; {3} Point(249,87)[hidden]; {4} Point(5,87)[hidden]; {5} Distance(1,2,268,197,'available fence ')[blue]; {6} Segment(1,2)[hidden,black]; {7} Segment(3,4)[hidden,black]; {8} Perpendicular(7,3)[hidden,black]; {9} Perpendicular(7,4)[hidden,black]; {10} Midpoint(6)[hidden,thick]; {11} Point on object(9,0.69509107)[hidden,thick]; {12} Segment(1,10)[hidden,thick,red]; {13} Parallel(7,11)[hidden,black]; {14} Point on object(12,0.28654972)[thick]; {15} Intersect(13,8)[hidden,thick]; {16} Circle(10,14)[hidden,thick,red]; {17} Polygon(3,15,11,4)[thick,red]; {18} Intersect2(6,16)[thick]; {19} Intersect1(6,16)[hidden,thick]; {20} Perpendicular(6,18)[hidden,thick,red]; {21} Segment(18,10)[hidden,black]; {22} Segment(1,18)[thick,blue]; {23} Perpendicular(6,19)[hidden,black]; {24} Segment(14,19)[thick,yellow]; {25} Segment(2,19)[thick,blue]; {26} Intersect(7,20)[hidden]; {27} Intersect(7,23)[hidden]; {28} Length(24,268,223,'Length(Segment width) = ')[black]; {29} Length(25,268,210,'Length(Segment height) = ')[black]; {30} Circle by radius(27,25)[hidden,black]; {31} Intersect1(23,30)[hidden]; {32} Intersect2(23,30)[hidden]; {33} Segment(31,27)[thick,blue]; {34} Parallel(7,31)[hidden,black]; {35} Intersect(20,34)[hidden]; {36} Segment(35,31)[thick,yellow]; {37} Segment(26,35)[thick,blue]; {38} Point on object(36,0.69444448)[hidden,thick]; {39} Point on object(37,0.33333337)[hidden,thick]; {40} AnimateButton(267,162,'Animate')(39,37,38,36)(1,1)(0,0)(0,0)[black,auto]; {41} Perpendicular(36,38)[hidden,black]; {42} Perpendicular(37,39)[hidden,black]; {43} Intersect(41,42); 13.0 10.0 0.0 60.999998940000026 49.00000211999996 171.0

]]> What is the ideal ratio of height to width for 25 meters of fencing?
Use the red dot to change the amount of fencing used for height versus width. Click the Sample button to measure the height, width, and area for this pen shape. Click the Clear button to erase all of your measurements.
When you're done, go back to page 1 to record your ratio. ]]> {1} Point(4,47)[hidden]; {2} Point(248,47)[hidden]; {3} Point(73,106)[hidden]; {4} Point(159,106)[hidden]; {5} Segment(2,1)[hidden,black]; {6} Segment(4,3)[hidden,black]; {7} Distance(4,3,267,157,'available fence ')[blue]; {8} Midpoint(6)[hidden,thick]; {9} Perpendicular(5,1)[hidden,black]; {10} Perpendicular(5,2)[hidden,black]; {11} Segment(4,8)[hidden,thick,red]; {12} Point on object(9,0.69509107)[hidden,thick]; {13} Point on object(11,0.21718633)[thick]; {14} Parallel(5,12)[hidden,black]; {15} Circle(8,13)[hidden,thick,red]; {16} Intersect(14,10)[hidden,thick]; {17} Intersect1(6,15)[hidden,thick]; {18} Intersect2(6,15)[thick]; {19} Polygon(2,16,12,1)[thick,red]; {20} Segment(3,17)[thick,blue]; {21} Segment(13,17)[thick,yellow]; {22} Perpendicular(6,17)[hidden,black]; {23} Segment(4,18)[thick,blue]; {24} Segment(18,8)[hidden,black]; {25} Perpendicular(6,18)[hidden,thick,red]; {26} Length(20,267,170,'Length(Segment height) = ')[black]; {27} Length(21,267,183,'Length(Segment width) = ')[black]; {28} Intersect(5,22)[hidden]; {29} Intersect(5,25)[hidden]; {30} Circle by radius(28,20)[hidden,black]; {31} Intersect2(22,30)[hidden]; {32} Intersect1(22,30)[hidden]; {33} Parallel(5,32)[hidden,black]; {34} Segment(32,28)[thick,blue]; {35} Intersect(25,33)[hidden]; {36} Segment(29,35)[thick,blue]; {37} Segment(35,32)[thick,yellow]; {38} Point on object(36,0.33333272)[hidden,thick]; {39} Point on object(37,0.69444412)[hidden,thick]; {40} Perpendicular(36,38)[hidden,black]; {41} Perpendicular(37,39)[hidden,black]; {42} AnimateButton(330,198,'Animate')(38,36,39,37)(1,1)(0,0)(0,0)[hidden,black,auto]; {43} Intersect(41,40); 10.0 5.0 50.0 33.660987809999966 18.67802438000004 86.0

]]> What is the ideal ratio of height to width for 50 meters of fencing?
Use the red dot to change the amount of fencing used for height versus width. Click the Sample button to measure the height, width, and area for this pen shape. Click the Clear button to erase all of your measurements.
When you're done, go back to page 1 to record your ratio. ]]> {1} Point(4,119)[hidden]; {2} Point(248,119)[hidden]; {3} Point(7,177)[hidden]; {4} Point(244,177)[hidden]; {5} Segment(2,1)[hidden,black]; {6} Segment(4,3)[hidden,black]; {7} Distance(4,3,267,229,'available fence ')[blue]; {8} Midpoint(6)[hidden,thick]; {9} Perpendicular(5,1)[hidden,black]; {10} Perpendicular(5,2)[hidden,black]; {11} Segment(4,8)[hidden,thick,red]; {12} Point on object(9,0.69509107)[hidden,thick]; {13} Point on object(11,0.80131769)[thick]; {14} Parallel(5,12)[hidden,black]; {15} Circle(8,13)[hidden,thick,red]; {16} Intersect(14,10)[hidden,thick]; {17} Intersect1(6,15)[hidden,thick]; {18} Intersect2(6,15)[thick]; {19} Polygon(2,16,12,1)[thick,red]; {20} Segment(3,17)[thick,blue]; {21} Segment(13,17)[thick,yellow]; {22} Perpendicular(6,17)[hidden,black]; {23} Segment(4,18)[thick,blue]; {24} Segment(18,8)[hidden,black]; {25} Perpendicular(6,18)[hidden,thick,red]; {26} Length(20,267,242,'Length(Segment height) = ')[black]; {27} Length(21,267,255,'Length(Segment width) = ')[black]; {28} Intersect(5,22)[hidden]; {29} Intersect(5,25)[hidden]; {30} Circle by radius(28,20)[hidden,black]; {31} Intersect2(22,30)[hidden]; {32} Intersect1(22,30)[hidden]; {33} Parallel(5,32)[hidden,black]; {34} Segment(32,28)[thick,blue]; {35} Intersect(25,33)[hidden]; {36} Segment(29,35)[thick,blue]; {37} Segment(35,32)[thick,yellow]; {38} Point on object(36,0.33333343)[hidden,thick]; {39} Point on object(37,0.69444400)[hidden,thick]; {40} Perpendicular(36,38)[hidden,black]; {41} Perpendicular(37,39)[hidden,black]; {42} AnimateButton(267,217,'Animate')(38,36,39,37)(1,1)(0,0)(0,0)[hidden,black,auto]; {43} Intersect(41,40); 5.0 40.0 200.0 23.543853735 189.91229253 237.0