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?

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?

• A. 49
• B. 97
• C. 113
• D. 64

Answer: (C)

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

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