document.write( "Question 1027075: Find the length of the shortest altitude of a triangle with sides of lengths 10, 24, and 26. \n" ); document.write( "
Algebra.Com's Answer #642420 by MathTherapy(10552)\"\" \"About 
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Find the length of the shortest altitude of a triangle with sides of lengths 10, 24, and 26.
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You have to 1st determine the area of the triangle.
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document.write( "This triangle represents a Pythagorean triple (10-24-26, or 5-12-13), which means that it's a right triangle. No sweat!
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document.write( "Using the 2 legs, you can find the area by applying the formula for the area of a triangle: \"%281%2F2%29bh\", which results in: \"%281%2F2%29%2810%29%2824%29\",
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document.write( "for an area of 120 sq units. Now, if this were NOT a right triangle, the easiest method to find the area is Heron's formula.\r
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document.write( "Now that we have the area, the shortest altitude, of the three, is the altitude that's drawn to the longest side, 
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document.write( "which in this case is the hypotenuse. After drawing the shortest altitude to the hypotenuse, we now apply the formula 
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document.write( "for the area of a triangle, once again, but this time, the base is the hypotenuse, and the altitude (shortest) is unknown. 
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document.write( "This gives us: \"%281%2F2%29bh+=+120\"
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document.write( "\"%281%2F2%29%2826%29h+=+120\"
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document.write( "\"13h+=+120\" 
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document.write( "h, or shortest altitude to this triangle = \"120%2F13\", or \"highlight_green%28matrix%281%2C4%2C+9%263%2F13%2C+or%2C+9.230769231%2C+units%29%29\" \n" );
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