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Given,

First side of the triangular field = 85 m

Second side of the triangular field = 154 m

Let the third side be x

Perimeter of the triangular field = 324 m

85 m + 154 m + x = 324 m

x = 324 – 239

x = 85 m

Let the three sides of the triangle be:

a = 85 m, b = 154n m and c = 85 m

Now,

s =

=

=

= 162

We know that,

Area of triangle =

=

=

=

= 11 × 9 × 7 × 2 × 2

= 2771 m²

We also know that,

Area of triangle =

2772 =

2772 = 77h

h =

h = 36 m

Therefore,

The length of the perpendicular from the opposite vertex on the side measuring 154 m is 36 m.