QQuestionMathematics
QuestionMathematics
**A computer randomly puts a point inside the rectangle. What is the probability that the point does not land in triangle T?**
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Answer
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Step 1:: Understand the problem
A triangle $T$ is inscribed in this rectangle with base $b$ and height $k$.
We need to find the probability that a randomly placed point in the rectangle does not fall in the triangle.
Step 2:: Calculate the area of the rectangle and triangle
A_{triangle} = \frac{1}{2} * b * k
The area of the rectangle is given by: The area of the triangle is given by:
Step 3:: Calculate the area of the region not covered by the triangle
A_{not triangle} = w * h - \frac{1}{2} * b * k
The total area of the rectangle minus the area of the triangle gives us the area of the region not covered by the triangle:
Step 4:: Calculate the probability
P(not triangle) = \frac{w * h - \frac{1}{2} * b * k}{w * h}
The probability that a randomly placed point does not fall in the triangle is equal to the ratio of the area not covered by the triangle to the total area of the rectangle:
Final Answer
The probability that a randomly placed point in the rectangle does not land in triangle $T$ is: P(not triangle) = \frac{w * h - \frac{1}{2} * b * k}{w * h}
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