Question
Find the length of the hypotenuse of a right triangle with legs of 8 and 15.
Responses
A 1717
B 1919
C 2121
D 2323
E 25 Find the length of the hypotenuse of a right triangle with legs of 8 and 15.
Responses
A 1717
B 1919
C 2121
D 2323
E 25
Responses
A 1717
B 1919
C 2121
D 2323
E 25 Find the length of the hypotenuse of a right triangle with legs of 8 and 15.
Responses
A 1717
B 1919
C 2121
D 2323
E 25
Answers
Answered by
GPT-4o mini
To find the length of the hypotenuse of a right triangle with legs of lengths 8 and 15, we can use the Pythagorean theorem, which states:
\[ c = \sqrt{a^2 + b^2} \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two legs.
Substituting in the values:
\[ a = 8, \, b = 15 \]
Now calculating:
\[ c = \sqrt{8^2 + 15^2} \]
Calculating the squares:
\[ 8^2 = 64 \]
\[ 15^2 = 225 \]
Adding them together:
\[ c = \sqrt{64 + 225} = \sqrt{289} \]
Taking the square root:
\[ c = 17 \]
Therefore, none of the options given (1717, 1919, 2121, 2323, 25) are correct.
The correct length of the hypotenuse is **17**.
\[ c = \sqrt{a^2 + b^2} \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two legs.
Substituting in the values:
\[ a = 8, \, b = 15 \]
Now calculating:
\[ c = \sqrt{8^2 + 15^2} \]
Calculating the squares:
\[ 8^2 = 64 \]
\[ 15^2 = 225 \]
Adding them together:
\[ c = \sqrt{64 + 225} = \sqrt{289} \]
Taking the square root:
\[ c = 17 \]
Therefore, none of the options given (1717, 1919, 2121, 2323, 25) are correct.
The correct length of the hypotenuse is **17**.