Question

a triangle has sides 35cm, 54cm and 61cm long. find its area, also find smallest of its altitude​

Answer 1

Answer:

Area - $939.1486 cm^{2}$ or $939.15 cm^2$ and Altitude to its smallest side -  $53.6656 cm$ ≈ $53.7 cm$

Step-by-step explanation:

a = 35cm

b = 54cm

c = 61cm

Semi - Perimeter (s) = $\frac{a+b+c}{2} = \frac{35 + 54 + 61}{2} = \frac{150}{2} = 75 cm$

∴ Area = $\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{75(75-35)(75-54)(75-61)} = \sqrt{75*40*21*14} = 939.1486 cm^{2} or 939.15 cm^2$

∴ Altitude to the smallest side = $\frac{2*Area}{Base} = \frac{2*939.1486}{35} = \frac{1,878.2972}{2} = 53.6656 cm$ or 53.7cm