Answer: The required value of x is 32.
Step-by-step explanation: We are given to find the length of the unknown side.
That is, x = ?
From the figure, we see a right-angled triangle with
length of the hypotenuse, h = 68 units,
length of the other two sides, a = 60 units and b = x.
Using Pythagoras theorem in the given right-angled triangle, we have
[tex]h^2=a^2+b^2\\\\\Rightarrow 68^2=60^2+x^2\\\\\Rightarrow x^2=68^2-60^2\\\\\Rightarrow x^2=4624-3600\\\\\Rightarrow x^2=1024\\\\\Rightarrow x=\pm32.[/tex]
Since x is the length of a side of the triangle, so it cannot be negative.
Therefore, x = 32 units.
Thus, the required value of x is 32.
