In terms of s, what is the function that gives the length of the hypotenuse h of an isosceles right triangle?

To determine the function that gives the length of the hypotenuse ( h ) of an isosceles right triangle in terms of the length of one leg ( s ), we can utilize the properties of such triangles.

In an isosceles right triangle, both legs are of equal length, meaning each leg measures ( s ). According to the Pythagorean theorem, the relationship between the legs and the hypotenuse can be expressed as:

[

h^2 = s^2 + s^2

]

This simplifies to:

[

h^2 = 2s^2

]

To find ( h ), we take the square root of both sides:

[

h = \sqrt{2s^2}

]

This further simplifies to:

[

h = s\sqrt{2}

]

Thus, the correct function relating ( h ) and ( s ) is ( h = s \cdot \sqrt{2} ). This reflects the relationship in an isosceles right triangle where, using the properties of 45-45-90 triangles, the hypotenuse is always the length of a leg multiplied by the square root of 2