document.write( "Question 173498: A garden lot is in the shape of a right triangle. The hypothenuse is 30 yds. longer than twice the length of the shorter leg, and the longer leg is 20 yds. longer than twice the length of the shorter leg. What are the lengths of the three sides? \n" ); document.write( "

Algebra.Com's Answer #128354 by nerdybill(7384) $\"\"$ $\"About$

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Apply the Pythagorean theorem:
\n" ); document.write( "Let x = shorter leg
\n" ); document.write( "then
\n" ); document.write( "30 + 2x = hypotenuse
\n" ); document.write( "20 + 2x = longer leg
\n" ); document.write( ".
\n" ); document.write( "From Pythagorean we have:
\n" ); document.write( "(30 + 2x)^2 = x^2 + (20 + 2x)^2
\n" ); document.write( "900 + 120x + 4x^2 = x^2 + 400 + 80x + 4x^2
\n" ); document.write( "900 + 120x = x^2 + 400 + 80x
\n" ); document.write( "500 + 120x = x^2 + 80x
\n" ); document.write( "500 + 40x = x^2
\n" ); document.write( "0 = x^2 -40x + 500
\n" ); document.write( "0 = (x-50)(x+10)
\n" ); document.write( ".
\n" ); document.write( "x = {50, -10}
\n" ); document.write( ".
\n" ); document.write( "Throw out the negative solution leaving us with:
\n" ); document.write( "x = 50 yards (shorter leg)
\n" ); document.write( ".
\n" ); document.write( "hypotenuse:
\n" ); document.write( "30 + 2x = 30 + 2(50) = 130 yards
\n" ); document.write( ".
\n" ); document.write( "Longer leg:
\n" ); document.write( "20 + 2x = 20 + 2(50) = 120 yards
\n" ); document.write( " \n" ); document.write( "

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