Question

the rectangular yard shown below has a circular pool and a triangular garden. a ball from an adjacent golf course lands at a random point within the yard. find the probability that the ball lands in the garden. the probability is □ (simplify your answer)

Explanation:

Step1: Calculate the area of the rectangle

The area formula for a rectangle is \(A = l\times w\). Here, \(l = 100\) ft and \(w = 50\) ft. So, \(A_{rectangle}=100\times50 = 5000\) square - feet.

Step2: Calculate the area of the triangle

The area formula for a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 8\) ft and \(h = 12\) ft. So, \(A_{triangle}=\frac{1}{2}\times8\times12=48\) square - feet.

Step3: Calculate the probability

The probability \(P\) that the ball lands in the garden (triangle) is given by the formula \(P=\frac{A_{triangle}}{A_{rectangle}}\). Substitute \(A_{triangle}=48\) and \(A_{rectangle}=5000\) into the formula: \(P = \frac{48}{5000}=\frac{12}{1250}=\frac{6}{625}\)

Answer:

\(\frac{6}{625}\)