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Old 08-29-2008, 01:03 AM
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Default Pentagon

In the adjoining figure, find the perimeter of the pentagon.
(a)17m
(b)22m
(c)27m
(d)32m
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Old 08-29-2008, 01:10 AM
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You have all the sides of the pentagon except the right-most one of the rectangle. The sum of the other sides is equal to 4 + 3 + 10 + 10 = 27. So your perimeter must be greater than 27 (since you have one more side to take into account and it's obviously greater than 0). There's only one option that's greater than 27.
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\int_0^{\infty} \prod_{n = 1}^{\infty} \left( \frac{1 + \left(\frac{x}{b+n}\right)^2}{1+  \left(\frac{x}{a + n - 1}\right)^2}\right) dx = \frac{\sqrt{\pi}}{2} \ \frac{\Gamma \! \left(a + \frac{1}{2}\right)}{\Gamma (a)} \ \frac{\Gamma (b+1)}{\Gamma \! \left(b + \frac{1}{2}\right)} \ \frac{\Gamma \! \left(b-a+\frac{1}{2}\right)}{\Gamma (b-a+1)}
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