Question

The perimeter of a triangle is 276 m and the product of differences of semi-perimeter and its respective sides is 496800.Find the area of the triangle.

Answer 1

Given (p-a)(p-b)(p-c) = 496800, and 2p =276
Area of Triangle = sqrt[p(p-a)(p-b)(p-c)]
                          = sqrt[138*496800]
                          = 8280 cm^2

Answer 2

Answer:

Perimeter of triangle = 276 m

⇒ a+b+c = 276

⇒ Semi- Perimeter = a+b+c/2

                                = 276/2     = 138 m

Now,

   (s-a) (s-b) (s-c) = 496800

Area of the triangle = √s (s-a) (s-b) (s-c)

                                 = √138 x 496800

                                  = 8680 cm²

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