Question

a rectangular board has an area of 648 square centimeters. the triangular part of the board has an area of 162 square centimeters. a dart is randomly thrown at the board. assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle? round to the nearest whole percent. 18% 25% 35% 50%

Explanation:

Step1: Recall probability formula

The probability $P$ of an event is given by $P=\frac{\text{Area of favorable region}}{\text{Total area}}$.

Step2: Identify areas

The area of the favorable region (the triangle) is $A_{triangle}=162$ square - centimeters, and the total area (the rectangle) is $A_{rectangle}=648$ square - centimeters.

Step3: Calculate probability

$P = \frac{A_{triangle}}{A_{rectangle}}=\frac{162}{648}=\frac{1}{4}=0.25$.

Step4: Convert to percentage

To convert the decimal to a percentage, we multiply by 100. So $P = 0.25\times100\% = 25\%$.

Answer:

B. 25%