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 triangular garden

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base is \(8\) ft and the height is \(10\) ft.

$$A_{garden}=\frac{1}{2}\times8\times10 = 40\space ft^{2}$$

Step2: Calculate the area of the rectangular yard

The formula for the area of a rectangle is \(A = length\times width\). Here, the length is \(100\) ft and the width is \(40\) ft.

$$A_{yard}=100\times40=4000\space ft^{2}$$

Step3: Calculate the probability

The probability \(P\) that the ball lands in the garden is given by the ratio of the area of the garden to the area of the yard.

$$P=\frac{A_{garden}}{A_{yard}}=\frac{40}{4000}=\frac{1}{100}$$

Answer:

\(\frac{1}{100}\)