Question

find the value of x in the triangle shown below. choose 1 answer. x = 2

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Here, \(a = 1\), \(b = 4\) and \(c=x\). So \(x^{2}=1^{2}+4^{2}\).

Step2: Calculate the right - hand side

\(1^{2}+4^{2}=1 + 16=17\). So \(x^{2}=17\).

Step3: Solve for \(x\)

Since \(x\) represents the length of a side of a triangle and must be positive, \(x=\sqrt{17}\).

Answer:

\(x = \sqrt{17}\)