Question

Find the area of a triangular field whose sides are 91 m, 98 m and 105 m in length. Find the height corresponding to the longest side.

Answer 1

Here, a = 91 m, b = 98 m and c =105 m

Therefore, S=91+98+1052=147

Area = √S(S−a)(S−b)(S−c)

= √147(147−91)(147−98)(147−105)

= √147×56×49×42

= √49×3×7×2×2×2×49×7×3×2

= 49×3×2×2×7 = 4116 m^2

Longest side = 105 m and base = 105 m

Let, h be the height corresponding to the longest side.

Area of the triangle = (1/2×base×height) sq units

⇒1/2×base×height=4116m^2
⇒105×height=2×4116

Therefore, height (h) = 78.4 m