document.write( "Question 375986: A ladder is two feet longer than the height of a certain wall. When the top of the ladder is placed against the top of the wall, the distance from the base of the ladder to the bottom of the wall is equal to the height of the wall. How high is the wall? \n" ); document.write( "
Algebra.Com's Answer #267781 by ankor@dixie-net.com(22740)\"\" \"About 
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A ladder is two feet longer than the height of a certain wall.
\n" ); document.write( " When the top of the ladder is placed against the top of the wall, the distance
\n" ); document.write( " from the base of the ladder to the bottom of the wall is equal to the height of the wall.
\n" ); document.write( "How high is the wall?
\n" ); document.write( ":
\n" ); document.write( "This is a right triangle problem, a^2 + b^2 = c^2
\n" ); document.write( "The distance from the base to the wall, and the height of the wall are given
\n" ); document.write( "as equal: a = b, the ladder is the hypotenuse, c = a+2
\n" ); document.write( ":
\n" ); document.write( "We can write the equation:
\n" ); document.write( "a^2 + a^2 = (a+2)^2
\n" ); document.write( ":
\n" ); document.write( "2a^2 = a^2 + 4a + 4
\n" ); document.write( "Combine on the left
\n" ); document.write( "2a^2 - a^2 - 4a - 4 = 0
\n" ); document.write( "a^2 - 4a - 4 = 0
\n" ); document.write( "Solve this using the quadratic formula
\n" ); document.write( "Positive solution; a = 4.828 ft height of the wall
\n" ); document.write( ":
\n" ); document.write( "6.828 ft = length of ladder
\n" ); document.write( "Seems kind of short, check solution by finding the ladder length
\n" ); document.write( "Ladder = \"sqrt%284.828%5E2+%2B+4.828%5E2%29\" enter into a calc
\n" ); document.write( "Ladder = 6.828; confirms our solution \n" ); document.write( "
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