If the space diagonal of cube C is 5 inches long, what is

[BTGModeratorVI]

If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C?

A. 5/(√6)
B. (5)√(2/3)
C. (5)√(3/2)
D. (5)√3
E. (5)√6

Answer: B
Source: Economist GMAT

[Brent@GMATPrepNow]

If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C?

A. 5/(√6)
B. (5)√(2/3)
C. (5)√(3/2)
D. (5)√3
E. (5)√6

Answer: B
Source: Economist GMAT

When it comes to 3-D diagonals, we can use this formula



In cube C, let's say that each side has side length x
So, the diagonal = √(x² + x² + x²) = √(3x²)
Here, we're told that the diagonal has length 5, so we can write:
5 = √(3x²)
Square both sides to get: 25 = 3x²
Divide both sides by 3 to get: 25/3 = x²
Square root both sides: √(25/3) = x
Or.... (√25)/(√3) = x
Simplify: 5/(√3) = x
We now know that each side in the cube has length 5/(√3)

Our goal is to find the diagonal of the BASE of cube C
The diagonal will be the hypotenuse of a right triangle in which each leg has length 5/(√3)
Using Pythagoras, we can say: diagonal² = [5/(√3)]² + [5/(√3)]²
So, diagonal² = 25/3 + 25/3
Simplify: diagonal² = 50/3
So, diagonal = √(50/3)
= √[(25)(2/3)]
= [√25][√(2/3)]
= 5√(2/3)
Answer: B

[swerve]

If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C?

A. 5/(√6)
B. (5)√(2/3)
C. (5)√(3/2)
D. (5)√3
E. (5)√6

Answer: B
Source: Economist GMAT

Space diagonal of cube \(= a \cdot \sqrt{3}\)
Base diaganol of cube \(= a \cdot \sqrt{2}\)

\(a\cdot \sqrt{3}=5\)

\(a=\dfrac{5}{\sqrt{3}}\)

\(a \cdot \sqrt{2} = 5 \cdot \sqrt{\dfrac{2}{3}}\)

Hence, B

[Scott@TargetTestPrep]

If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C?

A. 5/(√6)
B. (5)√(2/3)
C. (5)√(3/2)
D. (5)√3
E. (5)√6

Answer: B
Source: Economist GMAT

Recall that if s is the side length of a cube, then its space diagonal is s√3, and a diagonal of one of its faces is s√2.

Since the space diagonal of the cube is 5, we have:

s√3 = 5

s = 5/√3

Therefore, the diagonal of its base is 5/√3 * √2 = 5√2 / √3 = 5√(2/3).

Answer: B