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by [email protected] » Mon Apr 29, 2013 8:47 pm
Please tell me a simpler way to solve this question
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by Anju@Gurome » Mon Apr 29, 2013 9:13 pm
In the problem solving section. The first question involves a pentagon PQRST, PQ = 3, QR = 2, RS = 4, ST = 5, which of the following lengths 5, 10, and 15 could be the value of PT?
The length of any side of a polygon with n sides should be smaller than the sum of other (n - 1) sides. This is nothing but an extension of the known property of triangles : the length of any side of a triangle is always smaller than the sum of other two sides.

It'll be easier to visualize the situation rather than remembering this as a fact.
If the length of one side of a polygon is greater than or equal to the sum of the remaining sides, then all the points of the polygon will be on that side, i.e. there won't be any polygon at all; we will end up with a line segment.

Here, PQ + QR + RS + ST = 3 + 2 + 4 + 5 = 14
So, the length of 5th side should not be more than 14.

The correct answer is C.
Anju Agarwal
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