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Question

If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r cannot be equal to:

A
32
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B
34
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C
54
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D
74
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Solution

The correct option is C 74
5,5r,5r2 sides of triangle,
5+5r>5r2 ...(1)
5+5r2>5r ...(2)
5r+5r2>5 ...(3)
From (1) r2r1<0,
[r(1+52)][r(152)]<0
r(152,1+52) ...(4)
from (2),
r2r+1>0rR ...(5)
from (3),
r2+r1>0
So, (r+1+52)(r+152)>0
r(,1+52)(152,) ...(6)
from (4), (5), (6),
r(1+52,1+52)

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