The two rectangles above are similar, where x > 18. What is the value of x?

Rationale

x = 27.

In similar rectangles, the ratios of corresponding sides are equal. By setting up a proportion based on the given dimensions of the rectangles, we can solve for the value of x.

A (21) YOUR ANSWER

If x were 21, the ratio of the sides would not be consistent with the proportions required for similarity. This choice results in a ratio that does not match the established ratio of the corresponding sides of the rectangles.

B (24) YOUR ANSWER

Choosing 24 for x would also yield a ratio inconsistent with the similarity condition of the rectangles. The calculations would show that the dimensions do not maintain the proportion necessary for similarity, thus making this option invalid.

C (27) CORRECT

With x equal to 27, the ratios of the sides align perfectly, confirming that the rectangles are similar. This value satisfies the proportional relationship established by the dimensions of the rectangles, making it the correct answer.

D (33) YOUR ANSWER

If x were 33, the resulting ratio would exceed the proportional relationship required for similarity. This choice leads to an inconsistent ratio, disqualifying it as a valid solution for the problem.

E (54) YOUR ANSWER

Selecting 54 for x would result in a ratio that significantly diverges from the expected proportions of the rectangles. This discrepancy renders the option invalid as it does not satisfy the conditions of similarity.

Conclusion

The value of x must be 27 to maintain the proportional relationship between the sides of the similar rectangles. Other options fail to satisfy the requirements for similarity, as they do not yield consistent ratios. Thus, understanding the properties of similar shapes is crucial for determining correct values in geometric problems.

The two rectangles above are similar, where x > 18. What is the value of x?

x = 27.

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