Area Of Triangle

Algebra Level 3

Let a, b, c be the sides of triangle ABC.
Find the area of the triangle if :

a + b + c = 52.5
ab + bc + ca = 900.68
abc = 5044.956

NOTE : Round off your answer to 3 decimal places.

1 solution

Saurav Pal
Mar 27, 2014

Let $a + b + c = -p$
$ab + bc + ca = q$
$abc = -r$

Then by using Heron's formula , we get

AREA = $\frac{(4qp^{2} - p^{4} - 8.p.r)^{\frac{1}{2}}}{4}$
Therefore, the area of triangle ABC is 115.7047475 which on rounding off gives 115.705

Good solution.

Anuj Shikarkhane - 6 years, 11 months ago