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.
\[\text{In} \bigtriangleup \text{LNM}, \]
\[\frac{\text{LT}}{\text{NT}} = \frac{\text{LM}}{\text{NM}} \left( \text{ By angle bisector theorem } \right)\]
\[ \Rightarrow \frac{\text{LT}}{8} = \frac{6}{10}\]
\[\Rightarrow \text{LT} = \frac{8 \times 6}{10}\]
\[ = 4 . 8\]
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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