Answer: The correct option is (D) 10.6.
Step-by-step explanation: A right rectangular prism is shown in the given figure.
We are to find the length of DF to the nearest tenth of a centimeter.
Since the given figure is a right rectangular prism, so each angle of the figure is a right angle.
And, so in the modified attached figure, ΔGCF and ΔDCF are both right-angles triangles.
Also, CG = 10 cm, FG = 2 cm and DC = 3 cm.
From the right-angled triangle GCF, we have
[tex]CF^2=CG^2+FG^2~~~~~~~~~~~~~\textup{[Using Pythagoras theorem]}\\\\\Rightarrow CF^2=10^2+2^2\\\\\Rightarrow CF^2=100+4\\\\\Rightarrow CF^2=104.[/tex]
Again, from the right-angled triangle DCF, we get
[tex]DF^2=CF^2+DC^2~~~~~~~~~~~~~\textup{[Using Pythagoras theorem]}\\\\\Rightarrow DF^2=104+3^2\\\\\Rightarrow DF^2=104+9\\\\\Rightarrow DF^2=113\\\\\Rightarrow DF=\sqrt{113}\\\\\Rightarrow DF=10.63\sim 10.6.[/tex]
Thus, the length of DF is 10.6 cm.
Option (D) is CORRECT.
