Question

A triangle inside of a square. The top of the triangle divides a side of the square into 2 equal parts. The triangle is shaded and the area to the right of the triangle is shaded. A point is randomly chosen in the square. Which statements are true?

1) The point is more likely to be inside the shaded area to the right of the triangle.
2) The point is more likely to be inside the shaded triangle.
3) The point is equally likely to be inside the shaded area to the right of the triangle and inside the shaded triangle.
4) The point is equally likely to be outside the shaded area to the right of the triangle and outside the shaded triangle.

Answer 1

The point is equally likely to be inside the shaded area to the right of the triangle and inside the shaded triangle because both areas are equal, each occupying one fourth of the total area of the square.

The correct answer is 2).

Step-by-step explanation:

To determine which statement is true about the likelihood of a randomly chosen point being inside the shaded triangle or the shaded area to the right of it within a square, we need to consider the areas of both shaded regions.

Step-by-step Analysis:

1. Since the triangle is formed by dividing one side of the square into two equal parts, it is a right-angled isosceles triangle. The area of this triangle is half the product of the legs, which are equal to half the side of the square. So, the area of the triangle is ¼ of the total area of the square.
2. The remaining shaded area to the right of the triangle is also a right-angled isosceles triangle with the same dimensions as the first triangle, therefore occupying another ¼ of the total area of the square.
3. Since both shaded areas are equal, the probability of a randomly chosen point being in either of the shaded areas is the same.

Considering the above, statement 3) The point is equally likely to be inside the shaded area to the right of the triangle and inside the shaded triangle is true.

Statement 4) is not presented clearly enough to determine its truth without additional context or clarification.