Answer: The correct option is (B) 16 meters.
Step-by-step explanation: As shown in the attached figure, ABCD is a rectangle with length 63 m, width x m and diagonal 65 m.
We are given to find the value of x.
Since all the four angles of a rectangle are right angles, so triangle ABD will be a right-angled triangle, where
∠BAD = 90°, AB = 63 m, AD = x m and hypotenuse, BD = 65 m.
Using Pythagoras theorem, we have from triangle ABD that
[tex]BD^2=AB^2+AD^2\\\\\Rightarrow 65^2=x^2+63^2\\\\\Rightarrow x=\sqrt{65^2-63^2}\\\\\Rightarrow x=\sqrt{4225-3969}\\\\\Rightarrow x=\sqrt{256}\\\\\Rightarrow x=16.[/tex]
Thus, the value of x is 16 meters.
Option (B) is CORRECT.
