Question 1084406: A Gardener wishes to but a circular water feature (pool) in a right - angled triangular plot that has sides of 6m and 8m on its smallest sides. What is the radius in meters of the largest pool that will fit?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Since we know 2 shorter sides, we need to calculate the hypotenuse:
sqrt(6^2+8^2) = 10
:
Now we know all three sides, we can use Heron's formula to find the area.
Our perimeter is 10+8+6 = 24 and 24/2 = 12:
sqrt(12(12-10)(12-8)(12-6)) = 24 This is the area of the triangle
:
Radius of the inscribed circle:
(2a)/p, where a is the area and p the perimeter:
(2*24)/24 = 2 <--this is the radius of your incircle.
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Let me give you a shortcut in case you get another problem like this:
radius = (a+b-c)/2
r = (6+8-10)/2 = 2
The explanation for this method is lengthy, but the formula is short and sweet ;-)
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