Question

Please help me answer the first question! It would help me out a lot!!!!

Answer 1

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

Answer 2

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

`9^2+13^2=x^2\\ 81+169=x^2\\ 250=x^2\\ √(250)=x`

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.