Answer: 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
[tex]RT^2=ST \times TQ\\\\\Rightarrow x^2=9\times 16\\\\\Rightarrow x^2=144\\\\\Rightarrow x=\pm\sqrt{144}\\\\\Rightarrow x=\pm 12.[/tex]
Since length of a side cannot be negative, so x = 12.
Thus, the required value of x is 12.
