A computer randomly puts a point inside the rectangle. What is the probability that the point does not land in triangle T?

Concepts

Probability, Area of rectangle, Area of triangle, Geometric probability

Explanation

To find the probability that a point lands in triangle T when randomly placed in the rectangle, we find the ratio of the area of triangle T to the area of the rectangle. The presence of square S does not affect this, since the point is placed anywhere in the rectangle, and we are only asked about triangle T.

Step-By-Step Solution

Step 1

Find the area of the rectangle:

• Length = 6
• Height = 4
• Area of rectangle =6×4=24

Step 2

Find the area of triangle T:

• Base of triangle T = 3
• Height of triangle T = 4
• Area of triangle =21​×base×height
• Area of triangle T =21​×3×4=21​×12=6

Step 3

Calculate the probability:

• Probability =Area of rectangleArea of triangle T​=246​
• Simplify: 246​=41​

Final Answer

The probability that the point lands in triangle T is 41​​ (Option C).