Question

A diagonal of a cube measures the square root of 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.

Answer 1

This problem is just one about triangles! All of the faces of the cube are perpendicular to their adjacent faces, so the diagonal of one of the face will be a right angle with the edge of the cube. Thus, you can create a right triangle. Finally, use the Pythagorean Theorem to solve for x, the length of the side of the cube. You should get that the edge has a length of the square root of 50 centimeters, or 7.1 centimeters when rounded to the nearest tenth. Hope this helps!

Answer 2

The edge of the cube is 7.07 cm or 5√2 cm

Explanation:

Given : A diagonal of a cube measures the square root of 150 cm.

The diagonal of a face measures 10 cm.

To Find: What is the length, in centimeters, of an edge of the cube?

Solution:

Since the face of the cube is in the shape of square .

The diagonal of that face is 10 cm.

Since the formula of diagonal of square =
`√(2) a`

Where a is the side of square face

So,
`√(2) a=10`

`a=(10)/(√(2))`

`a=(10)/(√(2))* (√(2))/(√(2))`

`a=(10√(2))/(2)`

`a=5√(2)`

`a=7.07 cm`

Since the side of the square face is the edge of the cube

Hence the edge of the cube is 7.07 cm or 5√2 cm