Saturday, September 10, 2011

What is the area of a triangle with sides 2, 5 and 7

We use Heron's formula  to find the area when all 3 sides
a,b,c of a triangle is known.


But here 2+5 = 0. When the
sum of the 2 sides are equal to the third side, there is no formation of a triangle. It
becomes a triangle of zero area.


Ina triangle the sum of
any two sides should be greter than the third side.


But
heron's formula still holds good.


Heron's
formula:


Area of the triangle = sqrt{(s(s-a)(s-b)(s-c)}.
Where a, b and c are the length of the sides of the triangtle. s =
(a+b+c)/2.


Here a = 2 ,  b = 5 and c = 7. Therefore s =
(2+5+7)/2 = 7.


Area of triangle = sqrt{7(7-1)(7-5)(7-7)} =
sqrt{7(5*7*0)} = 0.

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