Question

The perimeter of a triangular field is 240 m its
two sides are 78 m and 50 m, then area of
triangular field is

Answer 1

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Hope it help u

Answer 2

Answer:

Area of the triangular field (A) = 1680 m²

Explanation:

Let a,b are c three sides of a

given triangle ,

a = 78m,

b = 50m,

c =?

i)Perimeter (P) = 240m [given ]

=> a+b+c = 240m

=> 78m + 50m + c = 240

=> 128 m + c = 240

=> c = 240 - 128

=> c = 112 m ---(1)

ii ) s = $\frac{P}{2}$

= $\frac{240}{2}$

=$120$ ----(2)

iii ) s-a = 120-78 = 42

s-b = 120-50 = 78

s-c= 128-112 = 8

Now ,

By Heron's Formula:

$\boxed {Area\: of\: a \: triangle=\sqrt{s(s-a)(s-b)(s-c)}}$

$A=\sqrt{120\times42\times70\times8}$

=$\sqrt{2^{2}\times3\times10\times2\times3\times7\times7\times 10\times2^{3}}$

= $\sqrt{2^{6}\times3^{2}\times7^{2}\times10^{2}}$

= $\sqrt{2^{3}\times3\times7\tims(10)^{2}}$

= $2^{3}\times3\times7\times10$

= $8\times3\times7\times10$

= $1680$

Therefore,

Area of the triangle (A) = 1680m²

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