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 triangle (garden)

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, base \(b = 10\) ft and height \(h=6\) ft.

$$A_{triangle}=\frac{1}{2}\times10\times6 = 30\space ft^{2}$$

Step2: Calculate the area of the rectangle (yard)

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

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

Step3: Calculate the probability

Probability \(P=\frac{\text{Area of garden}}{\text{Area of yard}}\)

$$P=\frac{30}{4000}=\frac{3}{400}$$

Answer:

\(\frac{3}{400}\)