Question

Calculate the length of the diagonal AB

Answer 1

AB =
`5√(3)` 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 =
`5√(2)`

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,
`x^(2) + 5^(2) = AB^(2)` =
`(5√(2) )^(2)` + 25

= 50 + 25

= 75

Therefore AB =
`√(75)` =
`5√(3)`

Answer 2

25
Step-by-step explanation:
No ok