Answer:
AB = [tex]5\sqrt{3}[/tex] cm
Step-by-step explanation:
As we can see from the figure, BCDE is a square with each corner equal to 90°.
So that, BDE is a right triangle with corner BED equal to 90°
As BDE is a right triangle, according to Pythagoras theorem, we have:
[tex]BD^{2} = BE^{2} +ED^{2} = 5^{2} + 5^{2} = 25 + 25 = 50[/tex]cm
As the diagram s the cube, so that it can be seen that AD is perpendicular to the surface BCDE
=> AD is perpendicular to BD
=> ADB is the right triangle with corner ADB equal to 90°.
As ADB is the right triangle, ccording to Pythagoras theorem, we have:
[tex]AB^{2} =AD^{2} + BD^{2} = 5^{2} +50 = 25 +50 = 75[/tex] cm
=> [tex]AB = \sqrt{75} = 5\sqrt{3}[/tex] cm
Conclusion: AB = [tex]5\sqrt{3}[/tex]cm
Cube is a three-dimensional shape where each of the six sides is a square .
Length of diagonal ab is 8.7 cm
Since, Each dimension of cube is 5 cm.
Length of diagonal AB is, [tex]=\sqrt{3}*side[/tex]
Length of diagonal AB = [tex]\sqrt{3}*5=5\sqrt{3}[/tex]
Length of diagonal AB = 8.7 cm
Learn more:
https://brainly.com/question/23476107
