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

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

• A. h = s/√2
• B. h = s * √2
• C. h = s^2
• D. h = 2s

Answer: (B)

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

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