Question

Find the value of x and y.

Answer 1

By the geometric mean theorem,

`(y)/(4)=(12)/(y) \\ \\ y^(2)=48 \\ \\ \boxed{y=4√(3)}`

So, by the Pythagorean theorem,

`12^(2)+(4√(3))^(2)=x^(2)\\\\144+48=x^(2)\\\\192=x^(2)\\\\\boxed{x=8√(3)}`