To solve the question of finding the length of one leg of an isosceles right triangle where the hypotenuse measures 10 inches, follow these steps:
1. Understand the properties of an isosceles right triangle: In an isosceles right triangle, the two legs (let's call them [tex]\(a\)[/tex]) are of equal length, and the hypotenuse (let's call it [tex]\(c\)[/tex]) is given. The relationship between the legs and the hypotenuse in this type of triangle can be derived from the Pythagorean theorem.
2. Use the Pythagorean theorem: In an isosceles right triangle, the Pythagorean theorem states that:
[tex]\[
a^2 + a^2 = c^2
\][/tex]
Since both legs are equal, we can simplify this to:
[tex]\[
2a^2 = c^2
\][/tex]
3. Solve for [tex]\(a\)[/tex]:
[tex]\[
a^2 = \frac{c^2}{2}
\][/tex]
Taking the square root of both sides gives:
[tex]\[
a = \sqrt{\frac{c^2}{2}} = \frac{c}{\sqrt{2}}
\][/tex]
Substitute the given hypotenuse ([tex]\(c = 10\)[/tex] inches):
[tex]\[
a = \frac{10}{\sqrt{2}}
\][/tex]
4. Simplify the expression: Although [tex]\(\frac{10}{\sqrt{2}}\)[/tex] is already simplified, let’s check if it matches one of the given options. Notice that none of the options involve further simplification or rationalization of the denominator.
5. Identify the correct option: The expression [tex]\(\frac{10}{\sqrt{2}}\)[/tex] corresponds directly to one of the given answer choices.
Therefore, the correct choice is:
[tex]\[
\boxed{\frac{10}{\sqrt{2}}}
\][/tex]
The length of one leg of the isosceles right triangle is indeed:
[tex]\[
\boxed{\frac{10}{\sqrt{2}}}
\][/tex]
Given the provided Python solution, the computed numerical result of this expression is approximately 7.071067811865475 inches.
