Question

Each leg of a 45-45-90 triangle has a length of 6 units. What is the length of its hypotenuse?

Answer 1

see the picture attached to better understand the problem

we know that

in the right triangle ABC

AB is equal to AC

`AB=AC=6units`

BC is the hypotenuse

Applying the Pythagorean Theorem

`BC^(2) =AB^(2)+AC^(2)\\ BC^(2) =6^(2) +6^(2) \\ BC^(2) =72\\ BC=√(72) \\ BC=6√(2) units`

therefore

the answer is

the length of the hypotenuse is
`6√(2)` units