document.write( "Question 1420: To reach a damsell in distress, a knight places a 13-foot ladder against the castle wall. The base of the ladder is 7 feet less than the distance from the top of the ladder to the ground. How high on the castle will the ladder reach? \n" ); document.write( "

Algebra.Com's Answer #449 by usyim88hk(158) $\"\"$ $\"About$

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So this will form a triangle:
\n" ); document.write( "(If you are in high level math, you will notice that it is a 5-12-13 triangle which has sides length of 5, 12 and 13, but if you don't, we will solve it now)
\n" ); document.write( "let x be the distance from the ladder to the ground
\n" ); document.write( "x^2 + (x-7)^2 = 13^2
\n" ); document.write( "x^2 + x^2 - 14x +49 = 169
\n" ); document.write( "2x^2 - 14x - 120 = 0
\n" ); document.write( "Now use the quardratic formula to solve:
\n" ); document.write( " $\"x=%2814%2B-sqrt%28%28-14%29%5E2-4%282%29%28-120%29%29%29%2F%282%282%29%29\"$
\n" ); document.write( " $\"x=%2814%2B-sqrt%281156%29%29%2F4\"$
\n" ); document.write( " $\"x=%2814%2B-34%29%2F4\"$
\n" ); document.write( "x = 48/4 or -20/4
\n" ); document.write( "x = 12 or -5
\n" ); document.write( "Because length of anything can not be a negative number, so 12 is the answer. \n" ); document.write( "

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