Rectangles H and J are similar. If the area of rectangle H is 14, what is the area of rectangle J?

7
3.15
Area = 14
Rectangle H
Rectangle J

1 answer

If rectangles H and J are similar, their areas are related by the square of the ratio of their corresponding side lengths.

Let's denote the area of rectangle H as \( A_H = 14 \) and the area of rectangle J as \( A_J \). In similar figures, if the ratio of the lengths of corresponding sides is \( k \), then the ratio of the areas will be:

\[ \frac{A_J}{A_H} = k^2 \]

Without knowing the ratio \( k \), we cannot directly calculate the area of rectangle J. However, assuming the areas are close in values, if the question is asking for potential values for the area of rectangle J and provided 7 and 3.15 as options, we can reason through potential length ratios.

To compute an area based on a potential ratio:

  1. If \( k^2 = \frac{7}{14} = 0.5 \), then \( k = \sqrt{0.5} \approx 0.707 \).
  2. If \( k^2 = \frac{3.15}{14} \approx 0.225 \), then \( k \approx 0.474 \).

Thus, the possible areas for rectangle J given the area of rectangle H is 14, can be either 7 or 3.15 based on the relationship of similarity, with the ratios leading to those areas.

In conclusion, since both options provided could represent areas of rectangle J based on different ratios, we would affirm that possible areas are:

  • 7 (if the ratio of side lengths is approximately 0.707)
  • 3.15 (if the ratio of side lengths is approximately 0.474)

Thus, it depends on the specific lengths corresponding to rectangles H and J.