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Guttering Coursework Question A length of guttering is made from a rectangular sheet of plastic, 20cm wide. What is the best position for the folds so that the guttering carries the maximum amount of water? 1st Method To find out the best place to fold two flaps on the 20cm sheet to find the best area. To do this we used trial and improvement so we went from 0 to 20 increasing the height by 2cm till we found the best area which was 10cm by 5cm we put the values into a table and then plotted a graph. Width(cm) Height(cm) Area(cm²) 20 0 0 18 1 18 16 2 32 14 3 42 12 4 48 10 5 50 8 6 48 6 7 42 4 8 32 2 9 18 0 20 0 We then did it for a 30 cm sheet Width(cm) Height(cm) Area(cm²) 30 0 0 28 1 28 26 2 52 24 3 72 22 4 88 20 5 100 18 6 108 16 7 112 15 7.5 112.5 14 8 112 12 9 108 10 10 100 8 11 88 6 12 72 4 13 52 2 14 28 0 30 0 We then tried to find a formulae that will find any area with x as the value this is what we found X/4 X/2 Angle Base Side X Y A A+B A+B/2 A+B/2*Y 0 10 5 0 5 10 20 10 50 10 10 5 0.868241 4.924038765 11.73648 21.73648 10.86824 53.51564 20 10 5 1.710101 4.698463104 13.4202 23.4202 11.7101 55.01948 30 10 5 2.5 4.330127019 15 25 12.5 54.12659 40 10 5 3.213938 3.830222216 16.42788 26.42788 13.21394 50.61232 50 10 5 3.830222 3.213938048 17.66044 27.66044 13.83022 44.44948 60 10 5 4.330127 2.5 18.66025 28.66025 14.33013 35.82532 70 10 5 4.698463 1.710100717 19.39693 29.39693 14.69846 25.13585 80 10 5 4.924039 0.868240888 19.84808 29.84808 14.92404 12.95766 90 10 5 5 3.06287E-16 20 30 15 4.59E-15 21 10 5 1.79184 4.667902132 13.58368 23.58368 11.79184 55.04315 22 10 5 1.873033 4.635919273 13.74607 23.74607 11.87303 55.04242 23 10 5 1.953656 4.602524267 13.90731 23.90731 11.95366 55.01699 24 10 5 2.033683 4.567727288 14.06737 24.06737 12.03368 54.96658 25 10 5 2.113091 4.531538935 14.22618 24.22618 12.11309 54.89094 26 10 5 2.191856 4.493970231 14.38371 24.38371 12.19186 54.78984 27 10 5 2.269952 4.455032621 14.5399 24.5399 12.26995 54.66304 28 10 5 2.347358 4.414737964 14.69472 24.69472 12.34736 54.51035 29 10 5 2.424048 4.373098536 14.8481 24.8481 12.42405 54.33159 21.5 10 5 1.832506 4.65208784 13.66501 23.66501 11.83251 55.04586 2nd Method We already had the angle the base and the side but we had to find out side x which was the extension at...

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