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10 November, 19:35

One end of a 13-foot-long ladder is resting on the top of a vertical wall. The distance from the foot of the ladder to the base of the wall is 7 feet less than the height of the wall. How high is the wall? Suggestion: Recall the Pythagorean theorem, which says for legs a and b and hypotenuse c of a right triangle that?

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  1. 10 November, 19:57
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    Answer: the height of the wall is 12 feet

    Step-by-step explanation:

    The ladder forms a right angle triangle with the vertical wall and the ground. The length of the ladder represents the hypotenuse, c of the right angle triangle. The height from the top of the ladder to the base of the vertical wall represents the leg, a of the right angle triangle.

    The distance from the bottom of the ladder to the base of the vertical wall represents the leg, b side of the right angle triangle.

    The distance from the foot of the ladder to the base of the wall is 7 feet less than the height of the wall. This means that

    a = b + 7

    To determine the height of the wall, a we would apply Pythagoras theorem which is expressed as

    Hypotenuse² = leg a² + leg b²

    13² = (b + 7) ² + b²

    169 = b² + 14b + 49 + b²

    2b² + 14b + 49 - 169 = 0

    2b² + 14b - 120 = 0

    Dividing through by 2, it becomes

    b² + 7b - 60 = 0

    b² + 12b - 5b - 60 = 0

    b (b + 12) - 5 (b + 12)

    b - 5 = 0 or b + 12 = 0

    b = 5 or b = - 12

    The distance cannot be negative so b = 5

    a = b + 7 = 5 + 7

    a = 12
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