What is the area (in unit squares) of the triangle enclosed by the graphs of 2x + 5y = 12, x + y = 3 and the x-axis?

Solution (By Examveda Team)

$$\eqalign{ & 2x + 5y = 12 \cr & x{\text{ - axis}}:y = 0\,;\,x = 6 \cr & x + y = 3 \cr & x{\text{ - axis}}:y = 0\,;\,x = 3 \cr & 2x + 5y = 12\,\,\,\,\,*1 \cr & \underline {\,x + y = 3\,\,\,\,\,\,\,\,\,\,\,\,*2\,} \cr & \,\,\,\,\,2x + 5y = 12 \cr & \,\,\,\,\,2x + 2y = 6 \cr & \underline {\,\, - \,\,\,\,\,\, - \,\,\,\,\,\,\,\, - \,\,\,\,} \cr & \,\,\,\,\,3y = 6 \cr & \,\,\,\,\,\,y = 2 \cr & \,\,\,\,\,\,x = 3 - 2 = 1 \cr} $$

$$\eqalign{ & {\text{Area of traingle}} = \frac{1}{2} \times {\text{base}} \times {\text{height}} \cr & = \frac{1}{2} \times 3 \times 2 \cr & = 3 \cr} $$