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, , of a right-angled triangle, given the lengths of the two legs. This problem uses the Pythagorean theorem.
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:
  • 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 and and hypotenuse , the theorem states:
3. Apply the theorem to the given triangle:
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 . Since length must be positive, we only consider the positive root:
The missing side length is 4.
The answer is 4.