Question

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

Answer 1

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 = √s(s - a)(s - b)(s - c)

⇒ √120 (120 - 50)(120 - 78)(120 - 112)

⇒ √120*70*42*8

⇒ √2822400

Area of the triangle = 1680 sq dm

Now,

Area of the triangle = 1/2*base*height

Height = 2*area/base

⇒ (2*1680)/50

⇒ 336/5

height = 67.2 dm