In a right triangle, if one leg has length $3$ units, the other leg has length $4$ units, what is the length of the side opposite the right angle (the hypotenuse)?

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

Answer: (A)

Verified step by step guidance

1. Identify the given sides of the right triangle: one leg is 3 units and the other leg is 4 units.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two legs. Mathematically, this is expressed as \(c^2 = a^2 + b^2\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs.
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 to find \(c^2 = 25\), then take the square root of both sides to find \(c = \sqrt{25}\), which gives the length of the hypotenuse.