Question

The size of the largest triangle in a triangle is 3 tines the size of the smallest one

a)True
b)False

Answer 1

The claim about triangle sizes is false as triangle proportions vary. The Pythagorean theorem is indeed used for vectors at right angles, a vector can form a right triangle with its components, and the result of adding vectors varies. The Three-Fifths Compromise is a historical fact about representation and taxation.

Step-by-step explanation:

The statement regarding the size of the largest triangle being 3 times the size of the smallest one is False. Without additional context or specific definitions of 'size' (whether referring to area or side lengths), this statement cannot be universally applied to all triangles. Each triangle's proportions are unique, and one cannot generalize their sizes in such a manner.

Let's address the questions provided:

1. Pythagorean theorem can indeed be used to calculate the length of the resultant vector when two vectors are at right angles to each other. This is because the two vectors and the resultant vector form the sides of a right-angle triangle. Therefore, the statement is True.
2. Without specific details about areas A1, A2, and A3, we cannot compare them. As such, no definitive answer is provided for the comparison of areas A1, A2, and A3.
3. It is True that a vector can form the shape of a right-angle triangle with its x and y components, as these components are perpendicular to each other by definition.
4. Adding five vectors does not necessarily result in a magnitude greater than adding just two. This depends on the direction and magnitude of each vector. Therefore, the statement can be True or False based on the vectors' specifics.

Regarding the Three-Fifths Compromise, the statement is True; it was a historical agreement that determined how slaves would be counted for purposes of representation and taxation.