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?

• A. $7$ units
• B. $4$ units
• C. $6$ units
• D. $5$ units

Answer: (D)

Verified step by step guidance

1. Identify that the triangle is a right triangle, which means the Pythagorean theorem applies. The theorem 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.
2. Label the legs of the triangle as \(a = 3\) units and \(b = 4\) units, and the hypotenuse as \(c\) units.
3. Write the Pythagorean theorem formula: \(c^2 = a^2 + b^2\).
4. Substitute the known values into the formula: \(c^2 = 3^2 + 4^2\).
5. Calculate the squares and sum them: \(c^2 = 9 + 16\), then find \(c\) by taking the square root of the sum: \(c = \sqrt{25}\).