Question

Study the two equilateral triangles. What factor is triangle 1 reduced to form triangle 2?

1) 0.5
2) 0.75
3) 1.25
4) 2.5

Answer 1

The student's question concerns finding the scale factor used to reduce one equilateral triangle to form another smaller equilateral triangle, which is determined through the ratio of their areas or side lengths.

Step-by-step explanation:

The question involves understanding the concept of scale factors in geometry and how to determine the factor by which one geometric figure is reduced to form another. Using the fact that the area of a triangle is given by ½ × base × height, if triangle 2 is a scaled down version of triangle 1, the scale factor can be determined by the square root of the ratio of their areas if the sides length ratio is not directly given. One important thing to remember is that when dealing with similar figures, the ratio of the areas is equal to the square of the scale factor used to reduce or enlarge the figure.