Question

16 fill in the blank 1 point which expression gives the length of jk in the triangle shown below? 24 31 choose your answer...

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \( \triangle JLK\) with legs \(JL = 24\) and \(LK=31\) and hypotenuse \(JK\), the Pythagorean theorem states that \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the lengths of the legs and \(c\) is the length of the hypotenuse. Here, \(a = 24\), \(b = 31\), and \(c=JK\). So, \(JK^{2}=24^{2}+31^{2}\).

Step2: Solve for \(JK\)

Take the square root of both sides of the equation \(JK^{2}=24^{2}+31^{2}\). Then \(JK=\sqrt{24^{2}+31^{2}}\).

Answer:

\(\sqrt{24^{2}+31^{2}}\)