Question

Find the of tringular filed whose side is 50m, 45m, 35m​

Answer 1

Correct Question -

Find the area of triangular field whose sides are 50m, 45m and 35m

Solution -

Let, the side of the triangular field be a, b and c.

Here,

a = 50m

b = 45m

c = 35m

For finding area of the triangular field first we need to find the semi-perimeter (s) of the triangular field,

Formula to find semi-perimeter (s),

$\boxed{s = \frac{a + b + c}{2} }$

Putting the values,

$s = \frac{50 + 45 + 35}{2}$

$s = \frac{130}{2}$

$s = 65$

Now,

By using Heron's formula

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

The above formula is used where it is not possible to find the height of the triangle easily.

$Area\: of \: triangular \: field = \sqrt{65(65 - 50)(65 - 45)(65 - 35)}$

$Area \: \: of \: triangular \: field = \sqrt{65 \times 15 \times 20 \times 30}$

$Area\: of \: triangular \: field = \sqrt{585000}$

$Area \: of \: triangular \: field = 764.852927.....$

$Area \: of \: triangular \: field = 764.9(approx)$

$\boxed{\boxed{{ \: Area\: of \: triangular \: field = 764.9 {m}^{2} }}}$