Question

The diagram shows 5cm×5cm×5cm cube calculate the length of the diagonal ab

Answer 1

Answer:

AB = $5\sqrt{3}$ 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:

         $BD^{2} = BE^{2} +ED^{2} = 5^{2} + 5^{2} = 25 + 25 = 50$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:

$AB^{2} =AD^{2} + BD^{2} = 5^{2} +50 = 25 +50 = 75$ cm

=> $AB = \sqrt{75} = 5\sqrt{3}$ cm

Conclusion: AB = $5\sqrt{3}$cm