Question

given the triangle below, what is the length of the hypotenuse? 3 cm 5 cm a 15 cm b $sqrt{34}$ cm c $sqrt{15}$ cm d 8 cm

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 3\) cm and \(b = 5\) cm, so \(c^{2}=3^{2}+5^{2}\).

Step2: Calculate \(3^{2}+5^{2}\)

\(3^{2}=9\) and \(5^{2}=25\), then \(3^{2}+5^{2}=9 + 25=34\). So \(c^{2}=34\).

Step3: Solve for \(c\)

Taking the square root of both sides, \(c=\sqrt{34}\) cm.

Answer:

B. \(\sqrt{34}\) cm