two sides of a triangular feild are in 85 cm
and 154 m in length and its perimeter
is 324m. Find the area of the feild
Answers
Step-by-step explanation:
ANSWER
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.