If the diagonal of the cube is 3 units, then the edge of the cube is …
August 22, 2021 | education
| Let’s denote the diagonal of the cube BC and consider the right-angled triangle ABC
Let AB = x unit.
Using the Pythagorean theorem for right-angled triangles, we compose the equation:
AB ^ 2 + AC ^ 2 = BC ^ 2 (*)
Find the length of the AC
To do this, consider a right-angled triangle ADC
Because all edges of a cube are equal, then AD = AC = AB = x units.
By the Pythagorean theorem
AD ^ 2 + DC ^ 2 = AC ^ 2
or
x ^ 2 + x ^ 2 = AC ^ 2
We get
AC ^ 2 = 2x ^ 2
Substituting the value AC ^ 2 into (*), we get
x ^ 2 + 2x ^ 2 = 3 ^ 2
3x ^ 2 = 9
x ^ 2 = 3
x = √3
Answer: √3 units.
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