Question

find the exact value of x.
x =
do the side lengths form a pythagorean triple?
yes
no

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(a = 4\), \(b = 6\), \(c = x\). So \(x^2 = 4^2 + 6^2\).

Step2: Calculate \(x^2\)

\(4^2 = 16\), \(6^2 = 36\), so \(x^2 = 16 + 36 = 52\).

Step3: Find \(x\)

Take square root: \(x = \sqrt{52} = 2\sqrt{13}\).

Step4: Check Pythagorean triple

Pythagorean triples are integers. \(4\), \(6\), \(2\sqrt{13}\) (not integer), so no.

Answer:

\(x = 2\sqrt{13}\); No (for the triple question)