Question

two sides of a triangular field are 85 M and 154 m in length and its perimeter is 324 m full stop find the area of the field and length of the perpendicular from opposite vertex on the side measuring 154 m

Answer 1

We know that,

Perimeter of a triangle = a + b + c

So,

324 = 154  + 85 + c

Therefore, c = 85m

By using Heron's Formula,

Area of triangle  =

$\sqrt{s(s - a)(s - b)(s - c)}$

Here,

a  =154m, b  = 85m and c = 85m

Therefore,

s = 154 + 85 + 852  = 162m.

Area of triangle ABC = $2772 {m}^{2}$

Area of the field = $2772 {m}^{2}$

2 ) Let the perpendicular = 154

ATQ,

Area of triangle  = 12 ( Base ) ( Height )

That is,

12 ( 154 ) k = 2772

77k = 2772

Therefore, k = $36 {m}^{2}$