(geometry e2020) what is the value of x?

 The required value of x is 12.

Step-by-step explanation:  We are given to find he value of x fro the figure shown.

We note from the figure that

triangle RSQ is aright-angled one, where

∠SRQ=90°, ST = 9, QT = 16  and  RT is the altitude drawn to the hypotenuse SQ.

We know that

if an altitude is drawn from the right-angle of a right-angled triangle to the hypotenuse, then the square of the altitude is equal to the product of the two segments of the hypotenuse.

So, in the given right-angled triangle RSQ, we get

Since length of a side cannot be negative, so x = 12.

Thus, the required value of x is 12.