In ∆MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7 MQ = 2.5 then Find QP.
Practice Set 1.2 | Q 3 | Page 14
In ∆MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7 MQ = 2.5 then Find QP.
Solution
\[\text{ In } \bigtriangleup PNM, \]
\[\frac{QM}{QP} = \frac{MN}{PN} \left( \text{ By angle bisector theorem } \right)\]
\[ \Rightarrow \frac{2 . 5}{QP} = \frac{5}{7}\]
\[\Rightarrow QP = \frac{2 . 5 \times 7}{5}\]
\[ = 3 . 5\]
Hence, the measure of QP is 3.5.
Solution:-
In triangle MNP, NQ is a bisector of ∠N.
Using the angle bisector theorem:
- QM/QP = MN/PN
Substituting given values:
- 2.5/QP = 5/7
Solving for QP:
- QP = (2.5 x 7)/5 = 3.5
Therefore, the length of QP is 3.5.
Chapter 1. Similarity- Practice Set 1.2 – Page 13
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