Find x. need with at least one of the problems

Hello from MrBillDoesMath!

x = 1/2

Discussion:

From the Pythagorean theorem

( sqrt(2) ) ^2 + x^2 = ( x+ 1) ^2           =>      as (sqrt(2))^2 = 2

2                   + x^2 = x^2 + 2x + 1    =>    subtract x^2 from each both sides

2 =      2x + 1                                     => subtract 1 from both sides

2-1 = 2x     =>

1 = 2x        =>

x = 1/2

Thank you,

MrB

it's

the radius is 2 times the diameter.

step-by-step explanation: