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# Consider the accompanying diagram. Which of the following statements

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Math Expert
Joined: 02 Sep 2009
Posts: 50044
Consider the accompanying diagram. Which of the following statements  [#permalink]

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29 Oct 2017, 01:08
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Difficulty:

5% (low)

Question Stats:

98% (00:57) correct 2% (01:20) wrong based on 52 sessions

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Consider the accompanying diagram. Which of the following statements is true?

(A) KM < KL
(B) KM < LM
(C) KL + LM < KM
(D) KL < LM
(E) LM < KL

Attachment:

2017-10-29_1207.png [ 5.97 KiB | Viewed 556 times ]

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Consider the accompanying diagram. Which of the following statements  [#permalink]

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29 Oct 2017, 11:45
Bunuel wrote:

Consider the accompanying diagram. Which of the following statements is true?

(A) KM < KL
(B) KM < LM
(C) KL + LM < KM
(D) KL < LM
(E) LM < KL

Attachment:
2017-10-29_1207.png

Triangle property: side lengths correspond with opposite angle measures. The longest side is opposite from the greatest angle. The shortest side is opposite from the smallest angle.

∠ L = 90
∠ M = 55
∠ K = 35
(90+55) = 145; (180-145) = ∠ K

Side opposite ∠ L, 90, is KM
Side opposite ∠ M, 55, is KL
Side opposite ∠ K, 35, is LM

Construct a compound inequality where sides opposite angles are listed from smallest to greatest

35 < 55 < 90, so
LM < KL < KM

Fastest way: look for shortest side, LM, on LHS (all signs are <).

That is Answer E, LM < KL
But (C) must be checked. Different format.

(C) KL + LM < KM
NO. Violates the triangle inequality rule: the sum of any two sides must be greater than the third side.

To check others:

(A) KM < KL
NO. Inequality says opposite. And 90 (angle opposite side KM) is not less than 55 (opposite KL)

(B) KM < LM
NO. Inequality says opposite. And 90 is not less than 35

(D) KL < LM
NO. Inequality says opposite. And 55 is not less than 35

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Consider the accompanying diagram. Which of the following statements &nbs [#permalink] 29 Oct 2017, 11:45
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