Orthohedron Analysis: Finding Rectangles in a 4×7×10 Rectangular Prism

To solve this problem, we'll follow these steps:

• Step 1: Identify the dimensions of each pair of rectangles given the orthohedron's dimensions.
• Step 2: Each face of a cuboid corresponds to a rectangle, with three distinct pairs of dimensions.
• Step 3: Identify all pairs of dimensions and count the pairs that form sets of rectangles.

Now, let's work through each step:
Step 1: The orthohedron's dimensions are given as $4$, $7$, and $10$.
Step 2: A cuboid (orthohedron) has three pairs of opposite rectangular faces:
- Pair 1: Two rectangles with dimensions $4 \times 7$.
- Pair 2: Two rectangles with dimensions $4 \times 10$.
- Pair 3: Two rectangles with dimensions $7 \times 10$.
Step 3: Count each of the pairs to verify the total number of rectangles formed.
We find there are 6 rectangles in total, with the dimensions specified above fulfilling the conditions for each face of the cuboid.

The solution to the problem is that the orthohedron is formed of:
2 Rectangles $4 \times 7$,
2 Rectangles $4 \times 10$,
2 Rectangles $7 \times 10$.

These dimensions and quantities match choice #3 in the answer options provided.