document.write( "Question 1127848: An extension ladder rests 4 m up a wall. If the ladder is extended a further 0.8 m without moving the foot of the ladder, then it will now rest 1 m further up the wall. How long is the extended ladder? \n" ); document.write( "

Algebra.Com's Answer #744291 by addingup(3677) $\"\"$ $\"About$

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So you have a right triangle where the long leg is the wall and the hypotenuse is the ladder (draw it, I did). The short leg of the triangle is the distance from the bottom of the wall to the bottom of the ladder.
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\n" ); document.write( "So the problem says: when the hypotenuse increases by 0.8m the long leg increases by 1m. Let the hypotenuse be h and the short leg be x (we know the length of the long leg, it's the height of the wall and it goes from 4 to 5 m.)
\n" ); document.write( "x² + 4² = h²
\n" ); document.write( "x² = h² - 16 (1)
\n" ); document.write( "When the ladder is extended by h + 0.8 meters it reaches 5 meters up the wall:
\n" ); document.write( "x² + 5² = (h + 0.8)²
\n" ); document.write( "x² = (h + 0.8)² - 25 (2)
\n" ); document.write( "Combine equations (1) and (2):
\n" ); document.write( "(h + 0.8)² - 25 = h² - 16
\n" ); document.write( "(h + 0.8)² - h² = 25 - 16
\n" ); document.write( "h² + 0.64 - h² = 9
\n" ); document.write( "1.6h = 8.36
\n" ); document.write( "h = 8.36 ÷ 1.6 = 5.225
\n" ); document.write( "The length of the extended ladder is: 5.225 + 0.8 = 6.025 meters.
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\n" ); document.write( "Happy learning! \n" ); document.write( "

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