the perimeter of a triangular field is 240 DM if two of its sides are 78 cm and 50 cm find the length of the perpendicular on the side of length 50 DM from the opposite vertex
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the key here is to use two different ways to calculate the area. the first method is to use the 3 sides since they are all known to calculate the area. the second method is to use the 1/2 bh formula which in this case will have the b and area and missing the h and that is what is required.
perimeter = 240 = 78+50+Y
Y = 240 - 128 = 112
s = 1/2 the perimeter = 120
Area = sqrt [s (s-a)(s-b)(s-c)] = sqrt (120 x 70 x 42 x 8) = 1680
Area = 1680 = 1/2 x 50 x h
h = 67.2
perimeter = 240 = 78+50+Y
Y = 240 - 128 = 112
s = 1/2 the perimeter = 120
Area = sqrt [s (s-a)(s-b)(s-c)] = sqrt (120 x 70 x 42 x 8) = 1680
Area = 1680 = 1/2 x 50 x h
h = 67.2
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