Question

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Answer 1

Answer: option C is the correct answer.

Step-by-step explanation:

In a cube, all the sides are equal.

The cube shown is 2 centimeters on all sides. The diagonal forms a right angle triangle with the sides of the cube with the diagonal representing the hypotenuse of the right angle triangle.

To determine the diagonal of the face of the cube,y, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore

y² = 2² + 2² = 4 + 4

y² = 8

y =√8

To determine the diagonal of the cube, x,

x² = 2² + y²

x² = 2² + (√8)² = 4 + 8

x² = 12

x √12 = 3.5 cm rounded to the nearest tenth.

Answer 2

Answer:

$2\sqrt{3}$ or 3.5 cm.

Step-by-step explanation:

Here we'll need a bit of right angle trig.

$z^{2} + y^{2} = x^{2}$, where x is the hypotenuse, and z and y are the opposite and adjacent sides. We can determine y by using the formula for the diagonal of a square, which is $s\sqrt{2 }$. So, y =  $2\sqrt{2 }$ and z = 2.

Therefore, we see that x = $\sqrt{(2\sqrt{2})^{2} + (2)^{2} } = \sqrt{8+4} =\sqrt{12} = 2\sqrt{3}$