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.

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!

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wifilethbridge wifilethbridge · Answer 2 · 2019-03-29T05:29:41+01:00

Answer:

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

Step-by-step 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 = [tex]\sqrt{2} a[/tex]

Where a is the side of square face

So, [tex]\sqrt{2} a=10[/tex]

[tex]a=\frac{10}{\sqrt{2}}[/tex]

[tex]a=\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]a=\frac{10\sqrt{2}}{2}[/tex]

[tex]a=5\sqrt{2}[/tex]

[tex]a=7.07 cm[/tex]

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