Final answer:
In a rectangle of 8 units by 4 units, the triangles ABE, BCF, and CDE are similar to △ABC. No right triangle dissimilar to △ABC is possible in this rectangle. Changing the rectangle's dimensions to 9 units by 3 units does not affect the number of similar triangles.
Step-by-step explanation:
In rectangle ABCD, with dimensions 8 units by 4 units, similar triangles can be identified based on their angles and sides. Since all right angles in a rectangle are equal, and the sides are proportional, the triangles ABE, BCF, and CDE are indeed similar to △ABC as option (a) suggests. All these triangles share the same angle measures and have sides in proportion. No right triangle that is not similar to △ABC can exist within this rectangle, affirming option (b), because all right triangles in this rectangle will share the characteristic angle measures of 90°, and the sides will be in proportion relative to each other.
If the dimensions of the rectangle were changed to 9 units by 3 units, the same principles apply. The number of similar triangles would remain the same, as indicated in option (b) since this change does not affect the internal angles or the proportional relationships of the sides within the right triangles that can be drawn inside this rectangle. As with any rectangle, similar triangles are determined by angle measures and the proportionality of sides, and changing the dimensions will maintain the rectilinear geometric properties and the similarities among the triangles formed within it.
Regarding the last pieces of the provided information, for the fencing example and the situation with the Moon, these are different contexts where the calculations of distance and size rely on understanding geometric properties, such as congruence and proportions to solve real-world problems.