The side of the edge of the cube is 7. 07cm
How to determine the length
Given that a diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.
Let's find the edge of the face
Note that the face of the cube is in the shape of square .
The diagonal of the face is 10 cm.
The formula for diagonal of square = [tex]\sqrt{2a}[/tex]
a is the side of the square face
We have that,
[tex]\sqrt{2a} = 10[/tex]
Make 'a' subject of formula
a = [tex]\frac{10}{\sqrt{2} }[/tex]
Find the surd of the equation, we have
a = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]
a = [tex]\frac{10\sqrt{2} }{2}[/tex]
a = [tex]5\sqrt{2}[/tex]
a = [tex]7. 07cm[/tex]
Thus, the side of the edge of the cube is 7. 07cm
Learn more about a cube here:
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