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

Explanation

Perimeter of the triangle `=240 dm`
Two sides (given)` = 78 dm \and\ 50 dm`
Third side of the triangle, `= 240 - (78 + 50)`
`= 240 dm - 128 dm= 112 dm`
`s = (a + b + c)/2`
`= (78 + 50 + 112)/2`
`= 240/2`
`s = 120 dm`
Area of the triangle `= sqrt(s(s - a)(s - b)(s - c))`
`=> sqrt(120 (120 - 50)(120 - 78)(120 - 112))`
`=>sqrt(120xx70xx42xx8)=>sqrt(2822400)`
Area of the triangle `= 1680dm^2`
Now, Area of the triangle`=1/2xxbasexxheight`
`Height = (2xxarea)/(base)`
`=>(2xx1680)/50`
`=>336/5,height = 67.2 dm`