Question

find the value of x in the triangle shown below.
choose 1 answer:
a ( x = 2 )
b ( x = 5 )
c ( x = sqrt{5} )
d ( x = sqrt{17} )

Explanation:

Step1: Apply Pythagorean theorem

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

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

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

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle (\(x>0\)), \(x=\sqrt{17}\).

Answer:

D. \(x = \sqrt{17}\)