Question

A right rectangular prism is shown. What is the length of DF¯¯¯¯¯ to the nearest tenth of a centimeter? Drag and drop the answer into the box. cm 9.810.210.410.6

Answer 1

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

$CF^2=CG^2+FG^2~~~~~~~~~~~~~\textup{[Using Pythagoras theorem]}\\\\\Rightarrow CF^2=10^2+2^2\\\\\Rightarrow CF^2=100+4\\\\\Rightarrow CF^2=104.$

Again, from the right-angled triangle DCF, we get

$DF^2=CF^2+DC^2~~~~~~~~~~~~~\textup{[Using Pythagoras theorem]}\\\\\Rightarrow DF^2=104+3^2\\\\\Rightarrow DF^2=104+9\\\\\Rightarrow DF^2=113\\\\\Rightarrow DF=\sqrt{113}\\\\\Rightarrow DF=10.63\sim 10.6.$

Thus, the length of DF is 10.6 cm.

Option (D) is CORRECT.

Answer 2

DF is 10.6 cm!!!!!!!!!!!!!!!!