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

Options

A. `7/4`
B. `3/2`
C. `5/4`
D. `3/4`

Answer

A

Explanation

`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`