Question

1. Find the area of the triangular field whose sides are 78 m, 50 m and 112 m. answer is 1680 m sq. how​

Answer 1

Answer:

1680 m²

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Answer 2

• 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 ) $s =\frac{P}{2}$

$= \frac{240}{2}$

• =120120 ----(2)

• iii ) s-a = 120-78 = 42

• s-b = 120-50 = 78

• s-c= 128-112 = 8

Now ,

By Heron's Formula:

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

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

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

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

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

$\tt= 2^{3}\times3\times7\times102$

$= 8\times3\times7\times108×3×7×10$

=16801680

Therefore,

• Area of the triangle (A) = 1680m²

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