two sides of a triangle field are 85m and 154m in lenght and it's perimeter is 324m find (i) the area of the field and (ii) the lenght of the perpendicular from the opposite vertex on the side measuring 154 m
Answers
Step-by-step explanation:
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=85m
Consider a=85m,b=154mandc=85m
We know that
S=
2
a+b+c
S=
2
85+154+85
By division
S=162m
We know that
Area
s(s−a)(s−b)(s−c)
By substituting the values
Area=
162(162−85)(162−154)(162−85)
So we get
Area=
162×77×8×77
It can be written as
Area=
2×9×9×7×11×2×2×2×7×11
On further calculation
Area=
11×11×9×9×7×7×2×2×2×2
We get
Area=11×9×7×2×2
By multiplication
Area=2772m
2
We know that
Area of the triangle =1/2×b×h
By substituting the values
1/2×154×h=2772
On further calculation
77×h=2772
So we get
h=2772/77
By division
h=36m
Therefore, area of the field is 2772m
2
and the length of the perpendicular from the opposite vertex on the side measuring 154m is 36m.