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12 December, 09:32

A ladder is leaning against a wall. The top of the ladder touches the wall at a height that is 5 feet less than the length of the ladder. The distance from the foot of the ladder to the wall is 10 feet less than the length of the ladder. How long is the ladder?

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  1. 12 December, 09:42
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    25 feet

    Explanation:

    Let the ladder be 'H' feet long

    Given;

    Ladder touches the wall at a height = H - 5 feet

    The distance from the foot of the ladder to the wall = H - 10 feet

    now a right angles triangle is formed by the system,

    where,

    Ladder forms the hypotenuse of the triangle

    Height of the wall is the perpendicular

    and, distance at the base is the base of the triangle formed

    Therefore,

    from the Pythagoras theorem, we have

    H² = (H - 10) ² + (H - 5) ²

    or

    H² = H² + 100 - 20H + H² + 25 - 10H

    or

    H² = 2H² + 125 - 30H

    or

    H² - 30H + 125 = 0

    on solving the quadratic equation, we get

    H² + ( - 5H - 25H) + 125 = 0

    or

    H (H - 5) - 25 (H - 5) = 0

    or

    (H - 5) * (H - 25) = 0

    therefore,

    we have

    H = 5 feet and H = 25 feet

    now,

    H = 5 is not possible as this length of the ladder will lead to the negative distance at the base and also, the height of the at the wall be zero

    Hence,

    the length of the ladder is 25 feet
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