Question

If in a triangle AB = 15 cm, BC = 14 cm and AC = 13 cm. Find the area of triangle ABC and hence its altitude on BC.

Answer 1

Answer:

Heya ‼

In ∆ABC, AB = 15 cm , BC = 13 cm and AC = 14 cm.

↪ By Heron's formula ,

S = ( A + B + C ) / 2S=(A+B+C)/2

S = ( 15 + 13 + 14 ) / 2S=(15+13+14)/2

S = 42 / 2S=42/2

S = 21S=21

↪ Now, area\:of\:triangle:-Now,areaoftriangle:−

= √S (S–A) (S–B) (S–C)

= √21 (21–15) (21–13) (21–14)

= √21 (6) (8) (7)

= √7056

= 84 cm^2=84cm

2

↪ Again,area\:of\:triangle,Again,areaoftriangle,

1/2×base×altitude=84 cm^21/2×base×altitude=84cm

2

1/2×14×altitude=841/2×14×altitude=84

7×altitude=847×altitude=84

altitude=84/7altitude=84/7

Altitude=12cmAltitude=12cm

Therefore, the area of ∆ABC is 84cm² and its altitude on AC is 12 cm.