The perimeter and area of a sector are $18 c m$ and $20 s q . c m$ respectively. Then the length of the arc is:

10 c m o r 8 c m

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10 c m o r 5 c m

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10 c m o r 4 c m

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20 c m o r 2 c m

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Solution

The correct option is A $10 c m o r 8 c m$
$l + 2 r = 18$
$\frac{l r}{2} = 20$
$l r = 40$
$l = \frac{40}{r}$
$18 = \frac{40}{r} + 2 r$
$r^{2} - 9 r + 20 = 0$
$(r - 4) (r - 5) = 0$
$r = 4$ or $r = 5$
$l = 8$ or $l = 10 c m$

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