The perimeter of Δ 𝑳𝑴𝑵 is 𝟑𝟐 𝐜𝐦. NX is the angle bisector of angle 𝑵, 𝑳𝑿 = 𝟑 𝐜𝐦, and 𝑿𝑴 = 𝟓 𝐜𝐦. Find 𝑳𝑵 and 𝑴𝑵.
A
LN = 9 cm and MN = 15 cm
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B
LN = 15 cm and MN = 9 cm
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C
LN = 12 cm and MN = 15 cm
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D
None of the above
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Solution
The correct option is A LN = 9 cm and MN = 15 cm Since NX is an angle bisector of angle 𝑵, by the angle bisector theorem, 𝑿𝑳:𝑿𝑴 = 𝑳𝑵: 𝑴𝑵; thus, 𝑳𝑵: 𝑴𝑵 = 𝟑: 𝟓.
Therefore, 𝑳𝑵 = 𝟑𝒙 and 𝑴𝑵 = 𝟓𝒙 for some positive number 𝒙. The perimeter of the triangle is 𝟑𝟐 𝐜𝐦.