Answer:
AB = [tex]5\sqrt{3}[/tex] cm
Step-by-step explanation:
The diagonal of the bottom square is the hypotenuse of two right triangles with legs 5 and 5
So, the length of that diagonal, say x, of a 45-45-90 triangle where x is the hypotenuse is x = [tex]5\sqrt{2}[/tex]
Now that diagonal is a leg of the right triangle where AB is the hypotenuse and 5 is the length of the other leg.
So, [tex]x^{2} + 5^{2} = AB^{2}[/tex] = [tex](5\sqrt{2} )^{2}[/tex] + 25
= 50 + 25
= 75
Therefore AB = [tex]\sqrt{75}[/tex] = [tex]5\sqrt{3}[/tex]
