MATH SOLVE

4 months ago

Q:
# Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the nearest tenth.A) JKM is a right triangle because KM = 15.3.B) JKM is a right triangle because KM = 18.2.C) JKM is not a right triangle because KM ≠ 15.3.D) JKM is not a right triangle because KM ≠ 18.2.

Accepted Solution

A:

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.