The length of the legs of a 45-45-90 Special Right Triangle are 5 inches. How long is the hypotenuse of the triangle?

Question 1 options:

15 inches

5√3– inches

5√2– inches

10 inches

Answer:

[tex]5\sqrt{2}[/tex]

Quiz results:

The length of the hypotenuse of a 45-45-90 Special Right Triangle is given by: Option C: 5√2 inches

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:

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:

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