Let a triangle be bounded by the lines \( L_{1}: 2 x+5 y=10 \); \( L_{2}:-4 x+3 y=12 \) and the ... VIDEO
Let a triangle be bounded by the lines \( L_{1}: 2 x+5 y=10 \); \( L_{2}:-4 x+3 y=12 \) and the line \( \mathrm{L}_{3} \), which passes through the point \( P(2,3) \), intersects \( L_{2} \) at \( A \) and \( L_{1} \) at \( B \). If the point \( P \) divides the line-segment \( A B \), internally in the ratio \( 1: 3 \), then the area of the triangle is equal to :
(a) \( \frac{110}{13} \)
(b) \( \frac{132}{13} \)
(c) \( \frac{142}{13} \)
(d) \( \frac{151}{13} \)
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