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Pythagorean Theorem: Find Hypotenuse with Radical Leg
Published on March 9, 2026
Geometry
Calculate the missing hypotenuse (h) of a right triangle given legs of 2 and $\sqrt{12}$ using the formula $a^2 + b^2 = h^2$. The solution is 4.
Question
Answer
The user has presented a math problem that requires finding the length of the hypotenuse,
1. Identify the given information:
The triangle is a right-angled triangle (indicated by the square symbol at one vertex).
The lengths of the two legs (the sides adjacent to the right angle) are:
The triangle is a right-angled triangle (indicated by the square symbol at one vertex).
The lengths of the two legs (the sides adjacent to the right angle) are:
- Leg
- Leg
The length of the hypotenuse (the side opposite the right angle) is.
2. State the Pythagorean Theorem:
For a right-angled triangle with legs
For a right-angled triangle with legs
3. Apply the theorem to the given triangle:
Substitute the known values into the formula, where
Substitute the known values into the formula, where
4. Calculate the squares:
5. Sum the squares of the legs:
6. Solve for
Take the square root of both sides to find
Take the square root of both sides to find
The missing side length
The answer is 4.