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If $A$ and $B$ are two points on the line $12 x + 5 y + 65 = 0$ , such that $O A = O B = 13$ then the area of the triangle is

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a

60 sq units

b

40 sq units

c

20 sq units

d

30 sq units

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detailed solution

Correct option is A

The perpendicular distance from a point Px1,y1 to the line ax+by+c=0 is ax1+by1+ca2+b2 The perpendicular distance from a point (0,0) to the line 12x+5y+65=0 is 120+50+65144+25=6513=5 Consider the triangle, Use Pythagorean Theorem to get the length of the base as 12+12=24 Hence the area of the triangle is 12(24)(5)=60 sq units

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