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Question

If 5,5r,5r2 are the side lengths of a triangle, then the possible value(s) of r is/are

A
32
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B
34
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C
52
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D
74
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Solution

The correct option is B 34

As 5,5r,5r2 are the sides of a triangle.
So, r>0

The triangle is possible if,
5+5r>5r2 (1)​​​​​
5r+5r2>5 (2)​​​​​
5r2+5>5r (3)​​​​​

From equation (1)
5r25r5<0
r2r1<0
r2r1=0r=1±52
So,
r2r1<0152<x<1+52
0<r<1+52 (4) [r>0]

From equation (2)
5r2+5r5>0
r2+r1>0
r>1+52 (5) [r>0]

From equation (3)
5r25r+5>0
r2r+1>0D=14=3<0xR

Therefore, from equation (4),(5) and (6), we get
(1+52)<r<(1+52)
r(0.618,1.618)

Hence, from the given options only r=32,34 satisfied above condition.

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