Question

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

Answer 1

In 45-45-90 triangles hypotenuse = x√2 [x=leg]

If leg = 6 units, then hypotenuse = 6√2 units.

Answer 2

Answer:
`6√(2)\ in`

Explanation:

Given: In a 45-45-90 triangle, the length of one of the legs= 6 in.

Let h be the hypotenuse of the given right triangle.

Since the two angles are equal (45°) in the given right triangle,Moreover in a triangle the side opposite to the equal angles are equal.

Therefore, the other leg of given right triangle = 6 in.

Thus by Pythagoras theorem, we get

`h^2=6^2+6^2=36+36\\\\\Rightarrow\ h^2=72\\\\\Rightarrow h=√(72)\\\\\Rightarrow h=6√(2)\ in`

Hence, the length of its hypotenuse =
`6√(2)\ in`