document.write( "Question 1064313: Given: ΔTSP, TS = SP = 10cm, TP = 12cm. Find: Three altitudes of ΔTSP. \n" ); document.write( "
Algebra.Com's Answer #679360 by rothauserc(4718)\"\" \"About 
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Let M be the point on TP where the bisector of angle TSP intersects TP
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\n" ); document.write( "Since triangle TSP is isosceles, SM is the perpendicular bisector of TP
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\n" ); document.write( "By Pythagorean Theorem,
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\n" ); document.write( "6^2 + SM^2 = 10^2
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\n" ); document.write( "SM^2 = 10^2 - 6^2 = 100 - 36 = 64
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\n" ); document.write( "SM = 8 cm
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\n" ); document.write( "Area(A) of triangle TSP = (1/2) * 12 * 8 = 48 cm^2
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\n" ); document.write( "now we can use area 48 cm^2 to solve for the other two altitudes
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\n" ); document.write( "48 = (1/2) * 10 * h
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\n" ); document.write( "5h = 48
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\n" ); document.write( "h = 9.6
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\n" ); document.write( "The three altitudes are 9.6 cm, 9.6 cm, 8 cm
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