Question

Find the hypotenuse of each isosceles right triangle when the legs are of the given measure.

Given = 6"

Answer 1

An isosceles triangle in this scenario is typically a 45/45/90 triangle, which means the two legs are 45 degrees and the hypotenuse is 90. So, we can come to the conclusion that both of the legs are the same, meaning they are both 45 degrees and 6 inches long.

The hypotenuse is radical two as big, so we would multiply 6 by radical two.
The hypotenuse is 6 radical 2.

Answer 2

The hypotenuse of given isosceles triangle is
`6√(2)` units.

Explanation:

According to the Pythagoras theorem, in a right angled triangle,

`hypotenuse^2=perpendicular^2+base^2`

The length of legs of an isosceles right angled triangle is 6 units.

Substitute perpendicular=6 and base=6 in the above formula.

`hypotenuse^2=6^2+6^2`

`hypotenuse^2=36+36`

`hypotenuse^2=72`

Taking square root both the sides.

`hypotenuse=√(72)`

`hypotenuse=6√(2)`

Therefore the hypotenuse of given isosceles triangle is
`6√(2)` units.