Answer:
C. JKM is not a right triangle because KM ≠ 15.3.
Step-by-step explanation:
We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.
In order to triangle JKM be a right triangle [tex]KM^{2}=JK^{2}+JM^{2}[/tex].
We will find length of side KM using our right triangles JLM and JLK as [tex]KM=KL+LM[/tex].
Using Pythagorean theorem in triangle JLM we will get,
[tex]LM=\sqrt{JM^{2}-JL^{2}}[/tex]
[tex]LM=\sqrt{8^{2}-5^{2}}[/tex]
[tex]LM=\sqrt{64-25}[/tex]
[tex]LM=\sqrt{39}=6.244997998\approx 6.24[/tex]
Now let us find length of side KL.
[tex]KL=\sqrt{JK^{2}-JL^{2}}[/tex]
[tex]KL=\sqrt{13^{2}-5^{2}}[/tex]
[tex]KL=\sqrt{169-25}[/tex]
[tex]KL=\sqrt{144}=12[/tex]
Now let us find length of KM by adding lengths of KL and LM.
[tex]KM=12+6.24=18.24[/tex]
Now let us find whether JKM is right triangle or not using Pythagorean theorem.
[tex]KM^{2}=JK^{2}+JM^{2}[/tex]
[tex]18.24^{2}=13^{2}+8^{2}[/tex]
[tex]18.24^{2}=169+64[/tex]
[tex]18.24^{2}=233[/tex]
Upon taking square root of both sides of equation we will get,
[tex]18.24\neq 15.264337522473748[/tex]
[tex]18.2\neq 15.3[/tex]
We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.
