document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #698509 by addingup(3677) $\"\"$ $\"About$

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Since we know 2 shorter sides, we need to calculate the hypotenuse:
\n" ); document.write( "sqrt(6^2+8^2) = 10
\n" ); document.write( ":
\n" ); document.write( "Now we know all three sides, we can use Heron's formula to find the area.
\n" ); document.write( "Our perimeter is 10+8+6 = 24 and 24/2 = 12:
\n" ); document.write( "sqrt(12(12-10)(12-8)(12-6)) = 24 This is the area of the triangle
\n" ); document.write( ":
\n" ); document.write( "Radius of the inscribed circle:
\n" ); document.write( "(2a)/p, where a is the area and p the perimeter:
\n" ); document.write( "(2*24)/24 = 2 <--this is the radius of your incircle.
\n" ); document.write( "-------------------------------------
\n" ); document.write( "Let me give you a shortcut in case you get another problem like this:
\n" ); document.write( "radius = (a+b-c)/2
\n" ); document.write( "r = (6+8-10)/2 = 2
\n" ); document.write( "The explanation for this method is lengthy, but the formula is short and sweet ;-) \n" ); document.write( "

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