Question 17

The value of x is 27.

The two rectangles being similar indicates that their corresponding sides are in proportion. Given the condition that x must be greater than 18, the calculations confirm that x equals 27.

A) 21

Option A is incorrect because 21 is less than 27, which does not satisfy the requirement of x being greater than 18. Additionally, it does not fit the proportional relationship needed for the rectangles to be similar.

B) 24

Option B is also incorrect. While 24 is greater than 18, it does not maintain the necessary ratio between the corresponding sides of the rectangles. Therefore, it fails to align with the properties of similar figures.

C) 27

Option C is correct as it meets the condition of x being greater than 18 and adheres to the proportional relationship required for the rectangles to be similar. This value maintains the necessary ratio between the sides of the two rectangles.

D) 33

Option D is incorrect because, although 33 is greater than 18, it does not satisfy the proportional relationship necessary for the rectangles' similarity. The calculation does not support this value as being correct in the context of the problem.

E) 54

Option E is incorrect since 54 is significantly greater than 27 and does not conform to the required proportionality between the rectangles. It fails to be the correct solution to the problem posed.

Conclusion

The correct answer is 27 because it satisfies both the condition of being greater than 18 and maintains the necessary proportions for the similarity of the rectangles. All other options either do not meet the greater than condition or fail to establish the required proportional relationship, confirming that 27 is the definitive solution.