The length of one leg of the triangle is 10√5 in.
What is Pythagoras theorem?
"The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides".
For the given situation,
The triangle that measures 45-45-90 angles indicate that the triangle is right-angled triangle and the other two sides are equal.
Formula for Pythagoras theorem,
c^2 = a^2 + b^2,
where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.
Hypotenuse, c = 10√5 in and
Other sides, a = b
By formula,
[tex]c^{2} =a^{2} + b^{2}[/tex]
⇒[tex](10\sqrt{5} )^{2} = a^{2} +a^{2}[/tex]
⇒[tex]500=2a^{2}[/tex]
⇒[tex]a^{2} = \frac{500}{2}[/tex]
⇒[tex]a^{2} = 250[/tex]
⇒[tex]a=\sqrt{250}[/tex]
⇒[tex]a=5\sqrt{10}[/tex]
Hence we can conclude that the length of one leg of the triangle is 10√5 in.
Learn more about Pythagoras theorem here
https://brainly.com/question/343682
#SPJ2
