Question

line segment jl is an altitude in triangle jkm. which statement explains whether jkm is a right triangle? round measures to the nearest tenth. \bigcirc jkm is a right triangle because kl + lm = 15.3. \bigcirc jkm is a right triangle because kl + lm = 18.2. \bigcirc jkm is not a right triangle because kl + lm \
eq 15.3. \bigcirc jkm is not a right triangle because kl + lm \
eq 18.2.

Explanation:

Step1: Calculate KL via Pythagoras

In right $\triangle JKL$:
$$KL = \sqrt{JK^2 - JL^2} = \sqrt{13^2 - 5^2}$$
$$KL = \sqrt{169 - 25} = \sqrt{144} = 12$$

Step2: Calculate LM via Pythagoras

In right $\triangle JLM$:
$$LM = \sqrt{JM^2 - JL^2} = \sqrt{8^2 - 5^2}$$
$$LM = \sqrt{64 - 25} = \sqrt{39} \approx 6.2$$

Step3: Sum KL and LM

$$KL + LM = 12 + 6.2 = 18.2$$

Step4: Verify right triangle condition

If $\triangle JKM$ were right-angled at $K$, $KM$ would equal $\sqrt{JK^2 + JM^2} = \sqrt{13^2 + 8^2} = \sqrt{233} \approx 15.3$. Since $KL+LM=18.2
eq 15.3$, $\triangle JKM$ is not right-angled.

Answer:

JKM is not a right triangle because $KL + LM
eq 15.3$