Question

If the sides of a triangles are 13 5 12 find the length of altiyude corresponding to the longest side as base by herons

Answer 1

Sol:

Sides of the triangle,

a = 20 cm, b = 21 cm, c = 29 cm

S = (a + b + c) / 2

  = (20 + 21 + 29) / 2

  = 35

Area of the triangle = √[s(s-a)(s-b)(s-c)]

= √[35(35-20)(35-21)(35-29)]

= √[(35)(15)(14)(6)]

= √44100

= 210

So, the area of the triangle is 210 sq cm

Area of the triangle considering the longest side as the base

= 1/2 × base × altitude

1/2 × 29 × altitude = 210

Altitude = (210 x 2) / 29

Altitude = 14.48 cm