Question : What is the area (in sq. units) of the triangle formed by the graphs of the equations $2x + 5y - 12=0, x + y = 3,$ and $y = 0$?
Option 1: 3
Option 2: 2
Option 3: 5
Option 4: 6
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Correct Answer: 3
Solution :
According to the question
Intersection point (P) of line $2x + 5y - 12 = 0$ and $y = 0$
⇒ $2x + 5 × 0 - 12 = 0$
⇒ $x = 6$
The point of intersection is P (6, 0).
Intersection point (Q) of line $x + y = 3$ and $y = 0$
⇒ $x + 0 = 3$
⇒ $x = 3$
The point of intersection is Q (3, 0).
Intersection point (R) of line $2x + 5y - 12 = 0$ and $x + y -3 = 0$
⇒ $2(3 -y) + 5y - 12 = 0$
⇒ $y = 2$ and $x = 1$
The point of intersection is R (1, 2).
Length of the base = PQ = 6 – 3 = 3 units
Height of point R from base = y coordinate of point R = 2 units
Area of triangle PQR = $\frac{1}{2}$ × 3 × 2 = 3 units
Hence, the correct answer is 3.
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