Question

Line segment JL is an altitude in triangle JKM. Triangle K J M is shown. Angle K J M is a right angle. An altitude is drawn from point J to point L on side K M to form a right angle. The length of K J is 13, the length of J L is 5, and the length of J M is 8. Which statement explains whether JKM is a right triangle? Round measures to the nearest tenth. JKM is a right triangle because KL + LM = 15.3. JKM is a right triangle because KL + LM = 18.2. JKM is not a right triangle because KL + LM ≠ 15.3. JKM is not a right triangle because KL + LM ≠ 18.2.

Answer 1

Answer:

JKM is not a right triangle because KL + LM ≠ 15.3.

Step-by-step explanation:

Given

$JK = 13$

$JL = 5$

$JM = 8$

Required

Determine if JKM is right-angles or not

Calculate length KL using Pythagoras theorem.

$JK^2 = JL^2 + KL^2$

$13^2 = 5^2 + KL^2$

Collect like terms

$KL^2 = 13^2 - 5^2$

$KL^2 = 144$

$KL = 12$

Calculate length LM using Pythagoras theorem.

$JM^2 = JL^2 + LM^2$

$8^2 = 5^2 + LM^2$

Collect like terms

$LM^2 = 8^2 - 5^2$

$LM^2 = 39$

$LM = \sqrt{39$

$LM = 6.2$

$KM = KL + LM$

$KM = 12 + 6.2$

$KM = 18.2$

If JKM is right-angled, then:

$KM^2 = JK^2 + JM^2$

$KM^2 = 13^2 + 8^2$

$KM^2 = 233$

$KM = \sqrt{233$

$KM = 15.3$

$15.3 \ne 18.2$

i.e

$KL + LM \ne 15.3$

Hence: JKM is not right-angled

Answer 2

Answer:

C-JKM is not a right triangle because KL + LM ≠ 15.3

Step-by-step explanation:

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