Question

find the length of side x in simplest radical form with a rational denominator.
(there is a right isosceles triangle with legs of length 8 and x, and the right angle is at the vertex where the two legs meet. the two legs are marked as equal with tick marks.)
answer attempt 1 out of 2
x =
(there is a square root symbol button and a submit answer button.)

Explanation:

Step1: Identify triangle type

The triangle is isosceles right - angled (two legs equal, right angle). Let the legs be \(a = 8\) and \(b = 8\), hypotenuse \(x\).

Step2: Apply Pythagorean theorem

Pythagorean theorem: \(x^{2}=a^{2}+b^{2}\). Substitute \(a = 8\), \(b = 8\):
\(x^{2}=8^{2}+8^{2}=64 + 64=128\)

Step3: Simplify radical

\(x=\sqrt{128}=\sqrt{64\times2}=\sqrt{64}\times\sqrt{2}=8\sqrt{2}\) (since \(x>0\) as it's a length)

Answer:

\(x = 8\sqrt{2}\)