Question

given the triangle below, what is the length of the hypotenuse? 2 cm 4 cm a 20 cm b 12 cm c $sqrt{12}$ cm d $sqrt{20}$ cm

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 2\) cm and \(b = 4\) cm. The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse.
So \(c^{2}=2^{2}+4^{2}\).

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

\(2^{2}+4^{2}=4 + 16=20\).

Step3: Find the hypotenuse

Since \(c^{2}=20\), then \(c=\sqrt{20}\) cm.

Answer:

D. \(\sqrt{20}\) cm