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

Answer 1

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

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