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?

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& 2x+5y=12\\ & x\text{ - axis}:y=0;x=6\\ & x+y=3\\ & x\text{ - axis}:y=0;x=3\\ & 2x+5y=12\ast 1\\ & \underline{x+y=3\ast 2}\\ & 2x+5y=12\\ & 2x+2y=6\\ & \underline{---}\\ & 3y=6\\ & y=2\\ & x=3-2=1\end{array}$$

$$\begin{array}{rl}& \text{Area of traingle}=\frac{1}{2}\times \text{base}\times \text{height}\\ & =\frac{1}{2}\times 3\times 2\\ & =3\end{array}$$