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There are two pentagons. The short sides of one is 8 and x - 3 and the long side is 16. The other pentagons short sides are 2 and 2.5 and the longs sides is 4.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
(2 points)
Since the polygons are similar, we can set up a proportion between corresponding sides.
For the first pentagon, the ratio of the length of the short side to the length of the long side is (8/(x-3))/16, which simplifies to (8/16)/(x-3) = 1/(x-3).
For the second pentagon, the ratio of the length of the short side to the length of the long side is (2/4)/(2.5) = 1/2.5.
Now we can set up the proportion: (1/(x-3)) = 1/2.5.
To solve for x, we can cross multiply: 2.5 = x - 3.
Adding 3 to both sides, we get: 5.5 = x.
Therefore, the value of x is 5.5.