Mathematics

Mathematics

Problem

Let a triangle be bounded by the lines

L_1: 2x + 5y = 10

;

L_2: -4x + 3y = 12

and the line

L_3

, which passes through the point

P(2, 3)

, intersect

L_2

at

A

and

L_1

at

B

. If the point

P

divides the line-segment

AB

, 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}{12}

(d)

\frac{151}{12}

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