In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value

Question

In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, if a=2 root3 , c=2b

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    2021-11-23T23:08:33+00:00

    In a right triangle, the sum of the squares of the legs is the square of the hypotenuse.

    So, you would have

     a^2+b^2=c^2

    If you plug the values, you have

     (2\sqrt{3})^2+b^2=(2b)^2

    So, you end up with a quadric equation in b:

     12+b^2=4b^2 \iff 3b^2=12 \iff b^2=4 \iff b=2

    So, the three sides are

     a=2\sqrt{3},\ b=2,\ c=4

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