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

For a right - triangle with legs \(a = 2\) cm and \(b = 4\) cm, and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\).
Substitute \(a = 2\) and \(b = 4\) into the formula: \(c^{2}=2^{2}+4^{2}\).
Calculate \(2^{2}=4\) and \(4^{2}=16\), so \(c^{2}=4 + 16\).

Step2: Simplify the equation

\(c^{2}=20\).
Take the square root of both sides: \(c=\sqrt{20}\) (since \(c>0\) for the length of a side of a triangle).

Answer:

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