Question 60

The area (in sq. unit) of the triangle formed in the first quadrant by the line 3x + 4y 12 is

Solution

Equation : $$3x + 4y = 12$$

Let the line cut x-axis at point B, => y-coordinate = 0

=> $$3x + 4(0) = 12$$

=> $$x = \frac{12}{3} = 4$$

=> $$B = (4,0)$$

Similarly, $$A = (0,3)$$

Thus, length of OA = 3 units and OB = 4 units

$$\therefore$$ Area of $$\triangle$$ OAB = $$\frac{1}{2} \times OA \times OB$$

= $$\frac{1}{2} \times 4 \times 3$$

= $$2 \times 3 = 6$$ sq. units

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