The length of the hypotenuse of a 45-45-90 Special Right Triangle is given by: Option C: 5√2 inches
What is Pythagoras Theorem?
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
For this case, we're specified that:
- The triangle is 45-45-90 Special Right Triangle,that means, two of its angles are of 45 degrees and one is of 90 degrees.
- The legs of the triangle (non-slant side, the sides which are perpendicular to each other) are of 5 inches length.
Thus, as shown in the diagram, the hypotenuse is AC.
Its length is found using the Pythagoras theorem as:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|AC|^2 = 5^2 + 5^2 = 25 + 25 = 50\\\\\text{Taking roots, but positive as AC is length, a non-negative quantity}\\\\|AC| = \sqrt{50} = \sqrt{25 \times 2} = \sqrt{5^2 \times 2} = 5\sqrt{2} \: \rm inches[/tex]
Thus, the length of the hypotenuse of a 45-45-90 Special Right Triangle is given by: Option C: 5√2 inches
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
