Question

In the cube above, $AB=4$. What is the perimeter of rectangle $ABCD$?

• A. $24$
• B. $16\sqrt{2}$ (approximately $22.63$)
• C. $16+4\sqrt{2}$ (approximately $21.66$)
• D. $8+8\sqrt{2}$ (approximately $19.31$)
• E. $4+8\sqrt{2}$ (approximately $15.31$)

Answer 1

The correct option is D $8+8\sqrt{2}$ (approximately $19.31$)

Given that $AB=4$. Since it is cube, all the sides of cube are equal .

So $AB=CD=4$.

We can see that the side $AD$ and $BC$ are diagonals of a square of side length $4$.

So $AD=BC=4\sqrt{2}$.

Therefore the perimeter of rectangle $ABCD$ is

$=AB+BC+CD+DA$

$=4+4\sqrt{2}+4+4\sqrt{2}$

$=8+8\sqrt{2}$.