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Two pentagons are shown.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
Since the two pentagons are similar, their corresponding sides are proportional.
Let's denote the side lengths of the bigger pentagon as 2a, 3a, 2a, 4a, and 5a (where a is a constant).
To find the value of x, we can compare the corresponding side lengths of the two pentagons.
In the smaller pentagon, the side lengths are x, 10, x, 15, and x.
Setting up a proportion:
(x / 2a) = (10 / 3a)
Cross-multiplying:
3a * x = 10 * 2a
Simplifying:
3ax = 20a
Dividing both sides by a:
3x = 20
Dividing both sides by 3:
x = 20 / 3
So the value of x is 20/3.
Answer: x = 20/3