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Question 3
What is the area (in square units) of the triangular region enclosed by the graphs of the equations x + y = 3, 2x + 5y = 12 and the x-axis?
Solution
x + y = 3
2x + 2y = 6Â ---(1)
2x +Â 5y = 12 ---(2)
From eq (1) and eq (2),
3y = 6
y = 2
So height = 2
y = 0 ---(3)
put the value of y in eq(1) and (2),
2x = 6
x = 3
And 2x = 12
x = 6
Area = $$\frac{1}{2} \times base \times height$$
= $$\frac{1}{2} \times (6 - 3) \times 2$$ = 3Â square units
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