Question

what is the length of the hypotenuse? a 81 cm b 25 cm c 3 cm d √53 cm 7 cm 2 cm

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 7\mathrm{cm}\) and \(b = 2\mathrm{cm}\).

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

\(a^{2}=7^{2}=49\) and \(b^{2}=2^{2}=4\), then \(a^{2}+b^{2}=49 + 4=53\).

Step3: Find the hypotenuse

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

Answer:

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