In a right triangle, if one leg has length $3$ units and the other leg has length $4$ units, what is the length of the hypotenuse (line segment $gh$)?

• A. $5$ units
• B. $6$ units
• C. $3$ units
• D. $4$ units

Answer: (A)

Verified step by step guidance

1. Identify the given information: the two legs of the right triangle have lengths 3 units and 4 units.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse length (c) is equal to the sum of the squares of the legs (a and b): \(c^2 = a^2 + b^2\).
3. Substitute the known leg lengths into the Pythagorean theorem: \(c^2 = 3^2 + 4^2\).
4. Calculate the squares of the legs: \$3^2 = 9\( and \)4^2 = 16\(, so \)c^2 = 9 + 16$.
5. Add the values and then take the square root of the sum to find the hypotenuse length: \(c = \sqrt{9 + 16}\).