Question

what is the length of the hypotenuse? 2 cm 7 cm a 81 cm b 25 cm c 3 cm d $sqrt{53}$ cm

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 2\) cm and \(b=7\) cm. The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So \(c^{2}=2^{2}+7^{2}\).

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

\(2^{2}+7^{2}=4 + 49=53\). So \(c^{2}=53\).

Step3: Find the value of \(c\)

Since \(c^{2}=53\), then \(c=\sqrt{53}\) cm.

Answer:

D. \(\sqrt{53}\) cm