Question

what is the length of x?

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 3\), \(b = 4\) and hypotenuse \(x\), the Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\).
So \(3^{2}+4^{2}=x^{2}\), which is \(9 + 16=x^{2}\).

Step2: Calculate \(x^{2}\) and \(x\)

\(9+16 = 25\), so \(x^{2}=25\). Taking the square root of both sides, since \(x\) represents the length of a side of a triangle (a non - negative value), \(x = 5\).

Answer:

5