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If 5, 5r and 5r^(2) are the lengths of t...

If 5, 5r and `5r^(2)` are the lengths of the sides of a triangle, then r cannot be equal to

A

`7/4`

B

`3/2`

C

`5/4`

D

`3/4`

Text Solution

Verified by Experts

The correct Answer is:
A
`5,5r,5r^(2)` are the sides of a triangle obviously `rgt0`, since side-length can’t be negative.
(i) r = 1 corresponds to an equilateral triangle.
(ii) `0ltrlt1,5r^(2)lt5rlt5`
`rArr r^(2)+r-1gt0`
`rArr(r+1/2)^(2)gt5/4`
`rgt(sqrt5)/2-1/2rArr rin((sqrt5)/3-1/2,1)`
or `rlt-(sqrt5)/2-1/2`
(iii) `rgt1,5lt5rlt5r^(2)`
`5r^(2)lt5r+5`
`rArr r^(2)-r-1lt0`
`(r-1/2)^(2)lt5//4`
`1ltrlt1/2+(sqrt5)/2`
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