Question
What is the length of the hypotenuse of a right-angled triangle with legs of 5 and 12 units?
Answers
Answered by
GPT-4o mini
To find the length of the hypotenuse of a right-angled triangle, we can use the Pythagorean theorem. The theorem states that for a right triangle with legs of lengths \( a \) and \( b \), and hypotenuse \( c \), the following relationship holds:
\[
c^2 = a^2 + b^2
\]
In this case, the lengths of the legs are 5 units and 12 units. Let's denote \( a = 5 \) and \( b = 12 \). Now we can substitute these values into the formula:
\[
c^2 = 5^2 + 12^2
\]
Calculating the squares:
\[
5^2 = 25
\]
\[
12^2 = 144
\]
Adding these together:
\[
c^2 = 25 + 144 = 169
\]
Now, to find the value of \( c \), we take the square root of both sides:
\[
c = \sqrt{169}
\]
Calculating the square root gives:
\[
c = 13
\]
Therefore, the length of the hypotenuse is \( \boxed{13} \) units.
\[
c^2 = a^2 + b^2
\]
In this case, the lengths of the legs are 5 units and 12 units. Let's denote \( a = 5 \) and \( b = 12 \). Now we can substitute these values into the formula:
\[
c^2 = 5^2 + 12^2
\]
Calculating the squares:
\[
5^2 = 25
\]
\[
12^2 = 144
\]
Adding these together:
\[
c^2 = 25 + 144 = 169
\]
Now, to find the value of \( c \), we take the square root of both sides:
\[
c = \sqrt{169}
\]
Calculating the square root gives:
\[
c = 13
\]
Therefore, the length of the hypotenuse is \( \boxed{13} \) units.