document.write( "Question 115254: a ladder is resting against a wall. the top of the ladder touches the wall at the height of 18 ft. find the length of the ladder if the length is 6 ft more than its distance from the wall \n" ); document.write( "

Algebra.Com's Answer #83855 by solver91311(24713) $\"\"$ $\"About$

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You have a right triangle. The right angle is where the floor meets the wall, one of the legs is the distance up the wall or 18 feet, the length of the ladder itself is the hypotenuse, we'll call that x, and the other leg is then x - 6.\r
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\n" ); document.write( "\n" ); document.write( "Time to ask Pythagoras for a little help. He says the hypotenuse squared is equal to the sum of the squares on the other two sides, so we can write:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2=18%5E2%2B%28x-6%29%5E2\"$
\n" ); document.write( " $\"x%5E2=324%2Bx%5E2-12x%2B36\"$
\n" ); document.write( " $\"x%5E2-x%5E2%2B12x=360\"$
\n" ); document.write( " $\"12x=360\"$
\n" ); document.write( " $\"x=30\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the ladder is 30 feet long, the base of the ladder is 24 feet from the wall along the floor, and the top of the ladder is 18 feet from the floor measured up the wall.\r
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\n" ); document.write( "\n" ); document.write( "Does that answer make sense? In other words, is a triangle with those dimensions a right triangle? If you divide each of those length values by 6, you will find that the proportions of the three sides are 3:4:5 -- and we know this to be a right triangle because $\"5%5E2=4%5E2%2B3%5E2\"$ \n" ); document.write( "

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