Question

find the value of x. answer in simplest form.
tell whether the side lengths form a pythagorean triple.
yes
no

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 12\), \(b = 12\) and hypotenuse \(x\), by the Pythagorean theorem \(a^{2}+b^{2}=x^{2}\).
Substitute \(a = 12\) and \(b = 12\) into the formula: \(x^{2}=12^{2}+12^{2}\).
Calculate \(12^{2}+12^{2}=144 + 144=288\).

Step2: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{288}\).
Simplify \(\sqrt{288}=\sqrt{144\times2}\).
Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 144\), \(b = 2\)), we get \(x = 12\sqrt{2}\).

Step3: Check Pythagorean triple

A Pythagorean triple consists of three positive integers \(a\), \(b\), \(c\) such that \(a^{2}+b^{2}=c^{2}\). Here \(a = 12\), \(b = 12\), \(x=12\sqrt{2}\approx16.97\) is not an integer.

Answer:

\(x = 12\sqrt{2}\), no.