Question

a right triangle has legs with length 3 and 4. what is the length of the hypotenuse? (enter your answer as a whole number) answer:

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 3\) and \(b = 4\), and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).
Substitute \(a = 3\) and \(b = 4\) into the formula: \(3^{2}+4^{2}=c^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(3^{2}=9\) and \(4^{2}=16\). Then \(9 + 16=c^{2}\), so \(c^{2}=25\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{25}\).

Answer:

5