Question

find the length of the third side. if necessary, write in simplest radical form. 8 8

Explanation:

Step1: Identify triangle type

It's a right - triangle with two legs of length 8. Let the hypotenuse (third side) be \( c \).

Step2: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \( a \) and \( b \) and hypotenuse \( c \), \( c^{2}=a^{2}+b^{2} \). Here, \( a = 8 \), \( b = 8 \). So \( c^{2}=8^{2}+8^{2}=64 + 64=128 \).

Step3: Simplify to find \( c \)

Take the square root of both sides: \( c=\sqrt{128}=\sqrt{64\times2}=8\sqrt{2} \).

Answer:

\( 8\sqrt{2} \)