Answer:
Step-by-step
From the problem statement, we know that point Q is equidistant from the sides of ZTSR, so if we draw perpendicular lines from point Q to each of the sides, the distances from Q to the sides will be equal. Let's call this distance d.
Using Pythagoras theorem, we can find the value of a:
a^2 = d^2 + 9^2
Similarly, we can find the value of c:
c^2 = d^2 + 16^2
Since Q is equidistant from both sides, we can set the right-hand sides of these equations equal to each other:
d^2 + 9^2 = d^2 + 16^2
Expanding and simplifying, we get:
d = 5√7
Now that we know the value of d, we can find the value of b:
b = TS - QS - QR
b = 25 - 5√7 - 20
b = 5 - 5√7
Finally, we can find the value of x by substituting the values we found into the equation we derived in the previous answer:
x = 338 / (b + c - 26)
Substituting in the values we found, we get:
x = 338 / ((5 - 5√7) + √(d^2 + 16^2) - 26)
Simplifying, we get:
x = 338 / (-5√7 + √(d^2 + 16^2) - 21)
Substituting in the value of d we found earlier, we get:
x = 338 / (-5√7 + √(5^2 + 7^2) - 21)
Simplifying, we get:
x = 13
Therefore, the answer is (d) 13.