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​Q . IF a , b , c FORM AN A.P WITH COMMON DIFFERENCE ‘d’ ( d not equal to 0) A ND x , y , z FORM G.P WITH COMMON RATIO ‘r’( r not equal to 1) , THEN THE AREA OF THE TRIANGLE WITH VERTICES – (a , x) , (b , y) AND (c,z) IS INDEPENDENT OF-( MORE THAN ONE OPTION CAN BE CORRECT) a b x r

​Q . IF a , b , c FORM AN A.P  WITH COMMON DIFFERENCE ‘d’ ( d not equal to 0) AND x , y , z  FORM   G.P WITH COMMON RATIO ‘r’( r not equal to 1) , THEN THE AREA OF THE TRIANGLE WITH VERTICES – (a , x) , (b , y) AND (c,z) IS INDEPENDENT OF-( MORE THAN ONE OPTION CAN BE CORRECT)
  1. a
  2. b
  3. x
  4. r
 
 
 
 
 
 

Grade:Select Grade

1 Answers

Y RAJYALAKSHMI
45 Points
6 years ago
a, b, c are in AP, ie, b = a + d, c = a + 2d 
x, y, z are in GP, ie. y = xr, z = xr2
 
The area of triangle  is ½ |a(y – z) + b(z – x) + c(x – y)|
Consider a(y – z) + b(z – x) + c(x – y)
= a(xr – xr2) + (a + d)(xr2 – x) + (a + 2d)(x – xr)
= axr – 2axr + 2axr – ax + dxr2 – dx + ax – axr + 2dx – 2dxr
= dxr2 + dx – 2dxr  which is independent of a, b, c, y, z 
 
 
 

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