SOLUTION: Find the diameter of the largest circular pond that could fit in a triangular garden with verticies at (18,54),(-27,36),(27,-18, where a unit represents 1m

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Question 1126088: Find the diameter of the largest circular pond that could fit in a triangular garden with verticies at (18,54),(-27,36),(27,-18, where a unit represents 1m
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!



first use distance formula to find the length of the sides:
a triangular garden with vertices at
A=(,),
B=(,),
C=(,)

find AB:
Solved by pluggable solver: Distance Between 2 points
The distance formula is . Plug in the numbers,

The distance is 48.4664832642105.




AB=c ->

find BC:
Solved by pluggable solver: Distance Between 2 points
The distance formula is . Plug in the numbers,

The distance is 76.3675323681471.



BC=a ->


find AC:
Solved by pluggable solver: Distance Between 2 points
The distance formula is . Plug in the numbers,

The distance is 72.5603197346869.



AC=b ->

Here is a formula in terms of the three sides:
If the sides have length ,, , we define the semi-perimeter s to be half their sum, so .



Given this, the radius is given using the following:



Take the square root of this expression to find .

meters

then, the diameter is meters


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