Question

A diagonal of a cube measures 150 cm. The diagonal of a face measures 10 cm.

What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth.
centimeters

Answer 1

Let's use the Pythagorean theorem to solve this problem.

If the diagonal of a face measures 10 cm, then we know that the edge of the cube is given by:

edge = 10/√2

Simplifying this expression, we get:

edge = 5√2

Now, we can use the diagonal of the cube to find the length of an edge. If the diagonal of the cube measures 150 cm, then we have:

edge√3 = 150

Substituting the expression we found for the edge, we get:

5√6 = 150/√3

Simplifying this expression, we get:

edge ≈ 19.2 cm

Rounding to the nearest tenth, we get the final answer:

The length of an edge of the cube is approximately 19.2 centimeters.

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Answer 2

Let s be the length of an edge of the cube. Then, by the Pythagorean theorem, we have:

s^2 + s^2 = (10 cm)^2

2s^2 = 100 cm^2

s^2 = 50 cm^2

s = sqrt(50) cm

Also, by the Pythagorean theorem, we have:

s^2 + s^2 + s^2 = (150 cm)^2

3s^2 = 22500 cm^2

s^2 = 7500 cm^2

s = sqrt(7500) cm

Therefore, the length of an edge of the cube is:

s ≈ 86.6 cm (rounded to the nearest tenth)