question_answer

The area of the triangle formed by the lines\[2x+3y=12,\,\,x-y-1=0\]and\[x=0\]is

A)  7.5 sq. units                   

B)  7 sq. units

C)  6.5 sq. units     

D)         6 sq. units

Correct Answer: A

Solution :

\[x=0\] is the equation of \[y-\]axis. \[2x+3y-12=0\] intersects at \[y-\]axis at \[B(0,\,\,4)\] which we get by putting\[x=0\]in\[2x+3y-12=0\]\[x-y-1=0\]intersects at\[D(0,\,\,-1)\] \[\therefore \] \[BD=5\]units      \[PL=3\]units \[\therefore \]Area of\[ABPD\]             \[=\frac{1}{2}BD\times PL\]             \[=\frac{1}{2}\times 5\times 3=7.5\]sq. units