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Question

In $$\triangle PQR$$, $$LM\parallel QR$$ and $$PM:MR=3:4$$. Calculate$$\cfrac{PL}{PQ}$$ and then $$\cfrac{LM}{QR}$$
235034_70fb296abc7d4bbeb4c1c6f3bb578752.PNG


A
PLPQ=LMQR=37
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B
PLPQ=LMQR=57
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C
PLPQ=LMQR=97
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D
PLPQ=LMQR=17
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Solution

The correct option is C $$\cfrac{PL}{PQ}=\cfrac{LM}{QR}=\cfrac{3}{7}$$
Given, $$LM \parallel QR$$, $$PM : MR = 3 : 4$$
$$\dfrac{PM}{MR} = \dfrac{3}{4}$$
$$\dfrac{PM + MR} {MR} = \dfrac{3+ 4}{4}$$
$$\dfrac{PR}{MR} = \dfrac{7}{4}$$
Now, In $$\triangle PLM$$ and $$\triangle PQR$$
$$\angle LPM = \angle QPR$$ (Common angle)
$$\angle PLM = \angle PQR$$ (Corresponding angles)
$$\angle PML = \angle PRQ$$ (Corresponding angles)
Thus, $$\triangle PLM \sim \triangle PQR$$ (AAA rule)
Hence, $$\dfrac{PL}{PQ} = \dfrac{LM}{QR} = \dfrac{PM}{PR}$$ (Corresponding sides)
$$\dfrac{PL}{PQ} = \dfrac{LM}{QR} = \dfrac{3}{7}$$
208620_235034_ans_1cf65a9b090148f483d37d8f469866fe.jpeg

Mathematics

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