We don't have enough information to determine the exact side length of either square A or square C, so we cannot directly calculate their areas. However, we can use the relationship between the areas of the squares to make some conclusions.
Since the area of square B is 64 square units, we know that its side length is √64 = 8 units.
Similarly, since the area of square C is 100 square units, we know that its side length is √100 = 10 units.
Square A is composed of square B and four identical triangles. We know the area of square B is 64 square units, so we need to determine the area of the four triangles to find the area of square A.
Each triangle has a base of 8 units (which is also the length of one side of square B) and a height of half the length of one side of square A. Let's call this length x.
The area of one triangle is (1/2) * 8 * x = 4x square units.
The total area of the four triangles is 4 times the area of one triangle, which is 16x square units.
Therefore, the area of square A is 64 + 16x square units.
We still don't know the exact value of x, but we can make some observations. Since square A is larger than square B, we know that x > 4. And since the triangles make up exactly half of square A (the other half being square B), we know that the area of square A is twice the area of the four triangles. Therefore:
64 + 16x = 2(16x)
64 + 16x = 32x
64 = 16x
x = 4
So the length of each side of square A is 8 + 2x = 16 units, and its area is 64 + 16x = 128 square units.
The length of CA is just the length of one side of square C, which is 10 units.