Using pythagorean theorem find a, and b, where a is twice of b and the hypotonuse is 5√5

Measure of Hypotaneous = 5√5

And it's already given that b = 2a

By using pythagoras theorem:

a²+ b² = (5√5)²

Let's substitute for b as 2a in above equation we'll get:

a² + (2a)² = (5√5)²

a² + 4a² = 125
5a² = 125
a² = 25
a = √25 = 5


Therefore,
a= 5
and
b = 2a = 2(5) = 10.