Answer:
The shortest path to take is
or ![34.64\ cm](https://tex.z-dn.net/?f=34.64%5C%20cm)
Step-by-step explanation:
<em>This question requires an attachment (See attachment 1 for question)</em>
Given
Cube Dimension: 20cm * 20cm
Required
Shortest path from A to B
For proper explanation, I'll support my answer with an additional attachment (See attachment 2)
The shortest path from A to B is Line labeled 2
But first, the length of line labeled 1 has to be calculated;
This is done as follows;
Since, the cube is 20 cm by 20 cm
(Pythagoras Theorem)
![Line1^2 = 2(20^2)](https://tex.z-dn.net/?f=Line1%5E2%20%3D%202%2820%5E2%29)
Take square root of both sides
![Line1 = \sqrt{2(20)^2}](https://tex.z-dn.net/?f=Line1%20%3D%20%5Csqrt%7B2%2820%29%5E2%7D)
Split square root
![Line1 = \sqrt{2} * \sqrt{20^2}](https://tex.z-dn.net/?f=Line1%20%3D%20%5Csqrt%7B2%7D%20%2A%20%5Csqrt%7B20%5E2%7D)
![Line1 = \sqrt{2} * 20](https://tex.z-dn.net/?f=Line1%20%3D%20%5Csqrt%7B2%7D%20%2A%2020)
![Line1 = 20\sqrt{20}](https://tex.z-dn.net/?f=Line1%20%3D%2020%5Csqrt%7B20%7D)
Next is to calculate the length of Line labeled 2
(Pythagoras Theorem)
Substitute ![Line1 = 20\sqrt{20}](https://tex.z-dn.net/?f=Line1%20%3D%2020%5Csqrt%7B20%7D)
![Line2^2 = (20\sqrt{2})^2 + 20^2](https://tex.z-dn.net/?f=Line2%5E2%20%3D%20%2820%5Csqrt%7B2%7D%29%5E2%20%2B%2020%5E2)
Expand the expression
![Line2^2 = (20\sqrt{2})*(20\sqrt{2}) + 20 * 20](https://tex.z-dn.net/?f=Line2%5E2%20%3D%20%2820%5Csqrt%7B2%7D%29%2A%2820%5Csqrt%7B2%7D%29%20%2B%2020%20%2A%2020)
![Line2^2 = 400*2 + 400](https://tex.z-dn.net/?f=Line2%5E2%20%3D%20400%2A2%20%2B%20400)
Factorize
![Line2^2 = 400(2+1)](https://tex.z-dn.net/?f=Line2%5E2%20%3D%20400%282%2B1%29)
![Line2^2 = 400(3)](https://tex.z-dn.net/?f=Line2%5E2%20%3D%20400%283%29)
Take square root of both sides
![Line2 = \sqrt{400(3)}](https://tex.z-dn.net/?f=Line2%20%3D%20%5Csqrt%7B400%283%29%7D)
Split square root
![Line2 = \sqrt{400} * \sqrt{3}](https://tex.z-dn.net/?f=Line2%20%3D%20%5Csqrt%7B400%7D%20%2A%20%5Csqrt%7B3%7D)
![Line2 = 20 * \sqrt{3}](https://tex.z-dn.net/?f=Line2%20%3D%2020%20%2A%20%5Csqrt%7B3%7D)
![Line2 = 20 \sqrt{3}](https://tex.z-dn.net/?f=Line2%20%3D%2020%20%20%5Csqrt%7B3%7D)
<em>The answer can be left in this form of solve further as follows;</em>
![Line2 = 20 * 1.73205080757](https://tex.z-dn.net/?f=Line2%20%3D%2020%20%20%2A%201.73205080757)
![Line2 = 34.6410161514](https://tex.z-dn.net/?f=Line2%20%3D%2034.6410161514)
<em> (Approximated)</em>
<em>Hence, the shortest path to take is </em>
<em> or </em>![34.64\ cm](https://tex.z-dn.net/?f=34.64%5C%20cm)