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16 December, 16:29

The two legs (labeled x) of the right triangle below have equal length. If the hypotenuse has length 5√2, solve for x.

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  1. 16 December, 20:28
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    x=5

    Step-by-step explanation:

    Other than using the plain special aspect of a 45-45-90 triangle where the legs are x, x, and x√2, you can solve for this.

    Since the two legs have equal length, they are both x. Using the pythagorean theorem:

    (x^2) + (x^2) = 50 (Because 5 squared is 25 and √2 squared is 2, multiplying them gives you 50).

    You can add (x^2) and (x^2) because they are the same terms (x squared).

    Simplifying like so gives you:

    2x^2=50

    Dividing by two on both sides:

    x^2=25

    Taking the square root of both sides:

    x=5
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