document.write( "Question 252398: In right triangle ABC where angle A is 90 degrees, AC = 3x and BC = 5x. if the perimeter of triangle ABC is 84, then what is x? \n" ); document.write( "

Algebra.Com's Answer #184263 by drk(1908) $\"\"$ $\"About$

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We have a right triangle with three sides: AC, BC, and AC. We know that AC = 3X, BC = 5X. If you drew this out, you would see that we are missing side AB. Let this side = KX, where K and X >= 1.
\n" ); document.write( "We apply the pythagorean theorem:
\n" ); document.write( " $\"%283x%29%5E2+%2B+%28kx%29%5E2+=+%285x%29%5E2\"$
\n" ); document.write( "this gives us
\n" ); document.write( " $\"9x%5E2+%2B+k%5E2x%5E2+%2B+25x%5E2\"$
\n" ); document.write( "divide out the X^2.
\n" ); document.write( " $\"9+%2B+K%5E2+=+25\"$
\n" ); document.write( "solve for K.
\n" ); document.write( "K^2 = 16
\n" ); document.write( "K = 4.
\n" ); document.write( "So, we are dealing with a 3x, 4x, 5x triangle. We need find to x knowing the perimeter = 84. We have
\n" ); document.write( "3x + 4x + 5X = 84
\n" ); document.write( "12x = 84
\n" ); document.write( "x = 7. \n" ); document.write( "

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