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Q.

If $5, 5 r, 5 r^{2}$ are length of sides of a triangle then $r$ can not be equal to

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a

$\frac{7}{4}$

b

$\frac{3}{4}$

c

$\frac{5}{4}$

d

$\frac{3}{2}$

answer is D.

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Detailed Solution

$5 + 5 r > 5 r^{2}$

$\Rightarrow r^{2} - r - r - 1 < 0 \Rightarrow r \in (\frac{- \sqrt{5} + 1}{2}, \frac{\sqrt{5} + 1}{2}) ∴ r \neq \frac{7}{4}$

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