Respuesta :

GoddessofDork

Since this is a right triangle, we can use the pythagorean theorem, [tex] leg^2+leg^2=hypotenuse^2 [/tex] , to solve for the hypotenuse as such:

[tex] 9^2+13^2=x^2\\ 81+169=x^2\\ 250=x^2\\ \sqrt{250}=x [/tex]

Even though √250 is the right answer, we can simplify it thanks to the product rule of radicals (√ab = √a x √b) as such:

√250 = √25 x √10 = 5√10

The length of the hypotenuse is 5√10, or approximately 15.81, cm.

PenguinHelper

To find the length of the hypotenuse, we need to use the Pythagorean Theorem. The Pythagorean Theorem states that in a triangle with legs a and b, and hypotenuse c, a² + b² = c². Since we know that the legs are 9 and 13, we can substitute these values into the equation. The equation becomes:

9² + 13² = c²

c² = 81 +169

c² = 250

Now we need to find √250. We can start to do this by finding the prime factorization of 250. The prime factorization of 250 is 5³ * 2. Since we see 5 three times, we can take it out once (because the quotient of 3 and 2 is 1 remainder one, but we don't look at the remainder). That means that the correct answer is: 5√2*5 = 5√10

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