3. Which of these situations is not possible if two shapes are similar?
A The perimeter of one is triple the perimeter of another, and the side
lengths are also triple.
B The perimeter of one is twice the perimeter of another, and the area
is four times as much.
C The angles of one and the angles of the other are the same, but
one area is three times as much as the other.
D The perimeter of one is triple the perimeter of another, and the area
is also triple.
how do you know
To determine which situation is not possible if two shapes are similar, we need to consider the properties of similar shapes.
Two shapes are similar if their corresponding angles are congruent and their corresponding side lengths are proportional. Therefore, we can conclude the following:
A) The perimeter of one is triple the perimeter of another, and the side lengths are also triple.
This situation is possible because if the side lengths are triple, the perimeter will also be triple.
B) The perimeter of one is twice the perimeter of another, and the area is four times as much.
This situation is possible. If the perimeter is twice as long, and the shapes are similar, the side lengths will be doubled, which makes the area four times as much.
C) The angles of one and the angles of the other are the same, but one area is three times as much as the other.
This situation is possible. Similar shapes have congruent angles, so if the angles are the same and the shapes are similar, the areas can differ by a scale factor.
D) The perimeter of one is triple the perimeter of another, and the area is also triple.
This situation is not possible if the shapes are similar. The perimeter is determined by the side lengths, and if the side lengths are triple, the perimeter will be triple. However, the area is determined by the square of the side lengths. If the side lengths are triple, the area will be nine times the original. Therefore, the area cannot be triple if the side lengths are triple and the shapes are similar.
Based on this analysis, we can conclude that option D is not possible if two shapes are similar.