https://file.aiquickdraw.com/mathbot/file/1726128515450ki5i1wuj.jpg

The image shows two adjacent rectangles. The heights and widths of these rectangles are provided, and the goal is to find the height of the smaller rectangle (denoted as \( x \)).

From the diagram:
1. The larger rectangle has a height of 2.856 and a width of 14.5.
2. The smaller rectangle has a width of 5.5, a given height of \( x \), and a total height of 3.447 from the base to the top.

To find \( x \), we use the fact that the total height (3.447) is the sum of the height of the larger rectangle (2.856) and the unknown \( x \).

Thus, we can write the equation:
\[
x + 2.856 = 3.447
\]
Now, solving for \( x \):
\[
x = 3.447 - 2.856 = 0.591
\]

So, the value of \( x \) is \( 0.591 \).

Would you like further details or have any questions? 

Here are some related questions:
1. What is the formula for the area of a rectangle?
2. How can you verify if two rectangles are similar based on dimensions?
3. How does the Pythagorean theorem apply to geometric problems like this?
4. How would the problem change if both rectangles were tilted?
5. What would the solution be if the height of the larger rectangle were unknown?

**Tip:** When solving geometric problems, always identify relationships between dimensions that allow for simplifying equations.

Find the height (x) of the smaller rectangle given the height of the larger rectangle (2.856), the total height from the base to the top (3.447), and the widths of both rectangles (14.5 and 5.5).

Learn how to find the unknown height (x) of a smaller rectangle using linear equations. This problem includes geometric concepts like height, width, and solving for unknown variables, ideal for students in Grades 6-8.

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