Question
How to find the length of the hypotenuse of a right-angled triangle with legs of 5 and 12 units?
Answers
GPT-4o mini
To find the length of the hypotenuse of a right-angled triangle, you can use the Pythagorean theorem. The 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).
The formula is:
\[ c^2 = a^2 + b^2 \]
In your case, the lengths of the legs are 5 units and 12 units. Therefore, you can substitute these values into the formula:
1. Identify the lengths of the legs:
- \( a = 5 \)
- \( b = 12 \)
2. Substitute into the formula:
\[
c^2 = 5^2 + 12^2
\]
3. Calculate the squares:
\[
c^2 = 25 + 144
\]
4. Add the results:
\[
c^2 = 169
\]
5. Take the square root of both sides to find c:
\[
c = \sqrt{169} = 13
\]
Therefore, the length of the hypotenuse is **13 units**.
The formula is:
\[ c^2 = a^2 + b^2 \]
In your case, the lengths of the legs are 5 units and 12 units. Therefore, you can substitute these values into the formula:
1. Identify the lengths of the legs:
- \( a = 5 \)
- \( b = 12 \)
2. Substitute into the formula:
\[
c^2 = 5^2 + 12^2
\]
3. Calculate the squares:
\[
c^2 = 25 + 144
\]
4. Add the results:
\[
c^2 = 169
\]
5. Take the square root of both sides to find c:
\[
c = \sqrt{169} = 13
\]
Therefore, the length of the hypotenuse is **13 units**.