Using the Pythagorean theorem, what is the prime number whose square root is the hypotenuse if the two legs of a right triangle measure 7 and 8 inches, respectively?

To find the hypotenuse of a right triangle using the Pythagorean theorem, one uses the formula ( c^2 = a^2 + b^2 ), where ( c ) is the length of the hypotenuse and ( a ) and ( b ) are the lengths of the legs of the triangle. In this case, the lengths of the legs are 7 and 8 inches.

First, calculate the squares of the legs:

• ( a^2 = 7^2 = 49 )

• ( b^2 = 8^2 = 64 )

Next, add these values together:

( c^2 = 49 + 64 = 113 )

Now, to find ( c ), we take the square root of ( c^2 ):

( c = \sqrt{113} )

The problem now focuses on identifying the prime number whose square is equal to ( c^2 = 113 ). Since 113 is not a perfect square, but rather is presented as the value of the hypotenuse squared, we can confirm that 113 itself is a prime number.

The other options provided do not meet the criteria:

• The number 49