document.write( "Question 1101135: ABC is a right triangle with area 30. The hypotenuse AC =13 and AB =5. Pick a point D in the interior of the triangle. X is the distance from D to the side AB, Y is the distance from D to the side AC, and Z is the distance from D to the side BC. Calculate 5X+13Y+12Z. \n" ); document.write( "

Algebra.Com's Answer #715727 by greenestamps(13215) $\"\"$ $\"About$

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With the given information, the length of BC is 12.

\n" ); document.write( "Consider triangles ADB, BDC, and CDA.

\n" ); document.write( "The area of triangle ADB is $\"%281%2F2%29%285%29%28x%29\"$
\n" ); document.write( "The area of triangle BDC is $\"%281%2F2%29%2812%29%28z%29\"$
\n" ); document.write( "The area of triangle CDA is $\"%281%2F2%29%2813%29%28y%29\"$

\n" ); document.write( "The area of triangle ABC is the sum of the areas of those three triangles:

\n" ); document.write( " $\"%285x%2F2%29%2B%2812z%2F2%29%2B%2813y%2F2%29+=+30\"$
\n" ); document.write( " $\"%285x%2B12z%2B13y%29%2F2+=+30\"$
\n" ); document.write( " $\"5x%2B13y%2B12z+=+60\"$
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