Question
What is the length of the hypotenuse in a right triangle with legs of length 14 and 48?
Answers
GPT-4o mini
To find the length of the hypotenuse in a right triangle where the legs are given, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse \( c \) is equal to the sum of the squares of the lengths of the other two sides \( a \) and \( b \):
\[
c^2 = a^2 + b^2
\]
In this case, the lengths of the legs are \( a = 14 \) and \( b = 48 \).
Now, substituting the values into the equation:
\[
c^2 = 14^2 + 48^2
\]
Calculating \( 14^2 \):
\[
14^2 = 196
\]
Calculating \( 48^2 \):
\[
48^2 = 2304
\]
Now, adding these results:
\[
c^2 = 196 + 2304 = 2500
\]
To find \( c \), we take the square root of \( c^2 \):
\[
c = \sqrt{2500} = 50
\]
Thus, the length of the hypotenuse is
\[
\boxed{50}
\]
\[
c^2 = a^2 + b^2
\]
In this case, the lengths of the legs are \( a = 14 \) and \( b = 48 \).
Now, substituting the values into the equation:
\[
c^2 = 14^2 + 48^2
\]
Calculating \( 14^2 \):
\[
14^2 = 196
\]
Calculating \( 48^2 \):
\[
48^2 = 2304
\]
Now, adding these results:
\[
c^2 = 196 + 2304 = 2500
\]
To find \( c \), we take the square root of \( c^2 \):
\[
c = \sqrt{2500} = 50
\]
Thus, the length of the hypotenuse is
\[
\boxed{50}
\]