Two sides of a triangular field are 85m and 154m in length and its perimeter is 324m. Find:
(i) The area of the field and
(ii) The length of the perpendicular from the opposite vertex of the side measuring 154m.
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.