Question

Two sides of a triangular field are 85 m and 154 m in length and its perimeter is 324 m. Find

(i) the area of the field and

(ii) the length of the perpendicular from the opposite vertex on the side measuring 154 m.

Answer 1

It is given that two sides of a triangular field are 85m and 154m

Consider the third side as x m

It is given that the perimeter = 324m

We can write it as

85 + 154 + x = 324

On further calculation we get

x = 324 – 85 – 154

By subtraction

x = 85 m

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

By multiplication

Area = 2772 m²

We know that

Area of the triangle = ½ × b × h

By substituting the values

½ × 154 × h = 2772

On further calculation

77 × h = 2772

So we get

h = 2772/77

By division

h = 36 m

Therefore, area of the field is 2772 m² and the length of the perpendicular from the opposite vertex on the side measuring 154m is 36m.