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

Let \(a = 3\) and \(b=5\). The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse.

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

\(a^{2}=3^{2}=9\) and \(b^{2}=5^{2}=25\), so \(a^{2}+b^{2}=9 + 25=34\).

Step3: Find the hypotenuse

Since \(c^{2}=34\), then \(c=\sqrt{34}\).

Answer:

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