document.write( "Question 333575: the flower garden has the shape of a right triangle. 5 ft of a perrineal border forms the hypotenuse of the triangle and one leg is 1 ft longer than the other legs, find the lengths of the legs\r
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Algebra.Com's Answer #239064 by jrfrunner(365) $\"\"$ $\"About$

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When you are dealing with a right triangle and you are trying to find lenght of the sides, you will most likely end up using the pythagorean theorem which states: $\"c%5E2=a%5E2%2Bb%5E2\"$ where c is the side opposite the right angle, and is called the hypotenuse.
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\n" ); document.write( "Given in your problem: c=5, a=x and b=x+1
\n" ); document.write( "so by the pythagorean theorem of a right triangle: $\"5%5E2+=+x%5E2+%2B+%28x%2B1%29%5E2\"$
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\n" ); document.write( " $\"25=x%5E2+%2B+%28x%5E2%2B2x%2B1%29\"$ (expanding the squared term)
\n" ); document.write( " $\"25=2x%5E2%2B2x%2B1\"$ (combining terms)
\n" ); document.write( " $\"0=2x%5E2%2B2x-24\"$ (putting the quadratic equation in standard form}}}\r
\n" ); document.write( "\n" ); document.write( " $\"0=x%5E2%2Bx-12\"$ (divide the whole thing by 2, to simplify the equation)
\n" ); document.write( "0=(x+4)*(x-3) (factor the expression on the right)
\n" ); document.write( "x=-4, x=3, since we are dealing with lengths, the negative value x= -4 is extraneous and can be trown out
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\n" ); document.write( "so, one side is a=x=3 and the other is b=x+1=4
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\n" ); document.write( "\n" ); document.write( "what you have is a special type of right triangle where the sides are in a ratio 3:4:5 \n" ); document.write( "

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