Question

The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm,and 50 dm ,find the length of the perpendicular on the side of length 50 dm from the opposite vertex.

Answer 1

perimeter of the triangle = 240dm
two sides of triangle are 78dm and 50dm
therefore third side={240-(50+78)}
=240-128
=112

by heron's formula area or triangle=168dm^2
therefore area of triangle= 1/2×b×h
=1680= 1/2×50×h
=1680=25×h
=1680/25=h
=h= 67.2 dm
therefore the length of perpendicular on the side of length 50dm is 67.2dm

Answer 2

Step-by-step explanation:

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