Problem
We are given two squares with areas of 256 and 625 square meters. If we join these two squares together, what will be the perimeter of the new figure?

Solution

To find the perimeter of the new figure, we need to determine the side lengths of the squares and then add them together.

Finding the side lengths of the squares

Let's assume the side length of the first square is 'a' meters. We are given that the area of the first square is 256 square meters. The formula for the area of a square is side length squared, so we can write the equation as:

a^2 = 256

To solve for 'a', we take the square root of both sides of the equation:

√(a^2) = √256
a = 16

Thus, the side length of the first square is 16 meters.

Similarly, let's assume the side length of the second square is 'b' meters. We are given that the area of the second square is 625 square meters. Using the same process, we find that the side length of the second square is 25 meters.

Finding the perimeter of the new figure

When we join the two squares together, they form a rectangle. The length of the rectangle is equal to the sum of the side lengths of the squares, and the width is equal to the side length of one of the squares.

The length of the rectangle is:
16 + 25 = 41 meters

The width of the rectangle is:
16 meters (since we can choose either square to determine the width)

Therefore, the perimeter of the new figure is double the sum of the length and width of the rectangle:

Perimeter = 2 * (41 + 16) = 2 * 57 = 114 meters

Conclusion
The perimeter of the new figure formed by joining the two squares with areas of 256 and 625 square meters is 114 meters.