Question

For a triangle whose sides re 50,78 and 112, respectively,then the length of the perpendicular from the opposite angle on the side 112cm

Answer 1

Answer:

Step-by-step explanation:

                       

                                  /\A

                               /  l   \

                            /     l      \

                         / .......l.........\

                       B        D         C

AB=50, BC=112, AC=78

let AD=x cm

area of triangle ABC = (1/2)×112×x = 56x cm²

also area of triangle ABC using heron's formula

Area = √(s(s-a)(s-b)(s-c))

now, s = (a+b+c)/2 = (50+78+112)/2 = 240/2 = 120

Area = √(120(120-50)(120-78)(120-112))

      = √(120×70×42×8)

     =10√(12×7×42×8)  

    = 10√(6×2×7×7×6×8)

    = 10×6×7√(2×8)

   = 420√16

   =420×4

  = 1680 cm²

equating both areas

56x = 1680

x= 1680/56

x=30 cm