Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Calculate the amount of fencing needed to enclose the lawn to the nearest tenth of a foot.
![### Geometry Practice Problem: Calculating Fencing Length
**Question 3**
Calculate the amount of fencing needed to enclose the lawn to the nearest tenth of a foot.
**Diagram Explanation:**
The diagram shows a sector of a circle with a central angle of 120 degrees and a radius of 14 feet. The sector is shaded to indicate the enclosed area.
**Diagram Details:**
- Central angle: 120°
- Radius: 14 feet
**Answer Options:**
- 205.3 ft
- 29.3 ft
- 57.3 ft
- 43.3 ft
To calculate the amount of fencing needed:
1. Compute the length of the arc.
2. Add the length of the two radii (which represent the straight edges of the sector).
**Formula for Arc Length (L) of a Sector:**
\[ L = 2\pi r \times \left(\frac{\theta}{360}\right) \]
where:
- \( r \) = radius of the circle = 14 feet
- \( \theta \) = central angle in degrees = 120°
Calculate the arc length:
\[ L = 2\pi \times 14 \times \left(\frac{120}{360}\right) \]
\[ L = 2\pi \times 14 \times \left(\frac{1}{3}\right) \]
\[ L \approx 29.32 \text{ feet} \]
Add the lengths of the two radii:
\[ \text{Total fencing} = L + 2r \]
\[ \text{Total fencing} = 29.32 + 2 \times 14 \]
\[ \text{Total fencing} = 29.32 + 28 \]
\[ \text{Total fencing} = 57.32 \]
Rounded to the nearest tenth, the amount of fencing needed is:
\[ 57.3 \text{ feet} \]
**Correct Answer:** 57.3 ft
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