The polygons are similar but not necessarily drawn to scale. Find the value of x.

To find the value of x in the larger polygon, we can use the property of similar polygons that states that the ratios of corresponding sides are equal.

The side lengths of the larger polygon are x, 3, 8, and 16. The side lengths of the smaller polygon are 25, 2, 4. Since the polygons are similar, we can set up the following ratios:

• For the sides of length 3: 3/2
• For the sides of length 8: 8/4
• For the sides of length 16: 16/25

Now we will look for a common ratio. Let’s take the sides of 8 and 4:

• From 8/4 = 2, we find that the ratio for similarity is 2.

Now apply this ratio for the corresponding sides to find x:

• x/25 = 2

Cross-multiplying gives us:

• x = 2 * 25
• x = 50

So, the value of x is 50. We can confirm this by checking the ratios of all sides to ensure they remain consistent:

• 3/2 = 1.5, 8/4 = 2, and 50/25 = 2.

Thus, all ratios confirm the polygons are similar, and we have correctly found that x = 50.