Question

find the value of x in the triangle shown below. choose 1 answer. a x = 4 b x = 8 c x = \sqrt{20} d x = \sqrt{34}

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 3\), \(c = 5\), and \(b=x\). So, \(3^{2}+x^{2}=5^{2}\).

Step2: Simplify the equation

\(9 + x^{2}=25\).

Step3: Solve for \(x^{2}\)

Subtract 9 from both sides: \(x^{2}=25 - 9\). So, \(x^{2}=16\).

Step4: Find \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle (\(x>0\)), \(x=\sqrt{16}=4\).

Answer:

A. \(x = 4\)