Question

find the length of the third side. if necessary, write in simplest radical form.

Explanation:

Step1: Aplicar el Teorema de Pitágoras

$$a^{2}+b^{2}=c^{2}$$
Donde \(c = 4\sqrt{5}\), \(b = 4\) y \(a\) es el lado desconocido.

Step2: Sustituir valores

$$a^{2}+4^{2}=(4\sqrt{5})^{2}$$

Step3: Calcular potencias

$$a^{2}+16 = 16\times5$$
$$a^{2}+16=80$$

Step4: Despejar \(a^{2}\)

$$a^{2}=80 - 16$$
$$a^{2}=64$$

Step5: Extraer raíz cuadrada

$$a=\sqrt{64}$$
$$a = 8$$

Answer:

\(8\)