In ∆LMN, ray MT bisects ∠LMN If LM = 6, MN = 10, TN = 8, then Find LT.
Practice Set 1.2 | Q 8 | Page 15
In ∆LMN, ray MT bisects ∠LMN If LM = 6, MN = 10, TN = 8, then Find LT.
Solution
[text{In} bigtriangleup text{LNM}, ]
[frac{text{LT}}{text{NT}} = frac{text{LM}}{text{NM}} left( text{ By angle bisector theorem } right)]
[ Rightarrow frac{text{LT}}{8} = frac{6}{10}]
[Rightarrow text{LT} = frac{8 times 6}{10}]
[ = 4 . 8]
Hence, the measure of LT is 4.8.
Answer:_
To find the measure of LT, we can use the angle bisector theorem in triangle LNM. We know that ray MT bisects angle LMN, so we have:
LT/NT = LM/NM
Substituting the given values, we get:
LT/8 = 6/10
Simplifying this equation, we get:
LT = (8 * 6)/10 = 4.8
Therefore, the measure of LT is 4.8 units.
Chapter 1. Similarity- Practice Set 1.2 – Page 15
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