Question

The two sides of a triangular field are 85m and 154m in length and its perimeter is 343m .Calculate the length of perpendicular from the opposite vertex on the side measuring 154m.​

Answer 1

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=2a+b+c

S=285+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=2772m2

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