document.write( "Question 80020: Find the altitude of the triangle.
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\n" ); document.write( "the dimensions are; 13, 13, and 10\r
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Algebra.Com's Answer #57425 by Earlsdon(6294) $\"\"$ $\"About$

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Find the altitude of the triangle whose sides are:
\n" ); document.write( "13, 13, and 10
\n" ); document.write( "This is obviously an isosceles triangle (at least two equal sides).
\n" ); document.write( "The altitude can be shown by dropping a perpendicular from the vertex angle (the angle between the two equal sides) to the base thus bisecting the base into two equal lengths of 5 units each.
\n" ); document.write( "Now the original triangle is shown as two congruent right triangles each having sides: 13 (the hypotenuse), 5 (the base), and h (the altitude).
\n" ); document.write( "You can find h using the Pythagorean theorem:
\n" ); document.write( " $\"13%5E2+=+5%5E2%2Bh%5E2\"$
\n" ); document.write( " $\"h%5E2+=+169-25\"$
\n" ); document.write( " $\"h%5E2+=+144\"$ Take the square root of both sides.
\n" ); document.write( " $\"h+=+12\"$ Discard the negative solution.
\n" ); document.write( "The altitude is 12 units. \n" ); document.write( "

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