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  e.  10√30

Step-by-step explanation:

In this right triangle geometry, all of the right triangles are similar. This means that the ratio of long side to hypotenuse is the same for all triangles:

  x/(10+50) = 50/x

Multiplying by 60x, we have ...

  x^2 = 3000

  x = 10√30 . . . . . take the square root. Matches choice E.

Comment on estimating

You're looking for x. Examining the figure, you see that x is the long side of the triangle with hypotenuse 10+50=60, so it will be shorter than that value. x is also the hypotenuse of the triangle with long side 50. So, x will be longer than 50.

The only answer choice with a value between 50 and 60 is choice E.

You don't even need to know how to find x. You only need to know that the hypotenuse is the longest side in a right triangle.

a 270° rotation about point p says on e d g e n u it y (had to space it out because it says it's a misspelling so i couldn't submit it