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Chapter 2: Problem 7

Find the perimeter of each figure. Rectangle: \(l=9.200\) in. \(, w=7.420\) in.

Short Answer

Expert verified
The perimeter of the rectangle is 33.240 inches.

Step by step solution

01

Identify the Perimeter Formula for a Rectangle

The perimeter of a rectangle can be found using the formula: \[ P = 2(l + w) \]where \( l \) is the length and \( w \) is the width of the rectangle.
02

Substitute the Known Values

Substitute the given values for length \( l = 9.200 \text{ in.} \) and width \( w = 7.420 \text{ in.} \) into the perimeter formula:\[ P = 2(9.200 + 7.420) \]
03

Perform the Addition Inside the Parentheses

Add the length and width together:\[ 9.200 + 7.420 = 16.620 \]
04

Calculate the Perimeter

Multiply the sum by 2 to find the perimeter:\[ P = 2 \times 16.620 = 33.240 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Perimeter Formula
Understanding the perimeter formula is essential in geometry, particularly for shapes like rectangles. The perimeter of a rectangle is the total distance around the outer edge of the shape. To calculate this, we use the formula:\[ P = 2(l + w) \]where \( P \) represents the perimeter, \( l \) is the length, and \( w \) is the width of the rectangle.
In simple terms, you first add the length and the width together, and then multiply the result by 2.
This formula works because a rectangle has two pairs of opposite sides that are equal in length. Calculating the perimeter involves accounting for each of these sides to understand the complete boundary of the rectangle.
Geometry
Geometry is a branch of mathematics that deals with the properties and relations of points, lines, surfaces, solids, and shapes. It's an ancient field that helps us measure, compare, and construct shapes in space.
When studying rectangles, geometry provides the formulas, like for perimeter and area, that help us understand their dimensions.
Geometrical principles are crucial when working in fields like architecture, engineering, and even in daily tasks that involve space management.

Why Study Rectangle Geometry?

Studying rectangle geometry helps you solve practical problems:
  • Design spaces: Architecturally, rectangles are common in floor plans and buildings.
  • Layout planning: Understanding rectangles assists in optimal storage solutions and furniture arrangement.
  • Calculation needs: From calculating material for framing to fencing a garden, mastering this is useful in real-world applications.
Rectangular Measurements
Rectangular measurements are crucial when dealing with any practical application involving rectangles. These measurements include the length and width of the rectangle, which are the basic dimensions needed to understand more complex properties like area and perimeter.

Measuring Length and Width

Measurements must be accurate to ensure correct calculations:
  • Use a ruler or tape measure for physical objects, ensuring the tool is straight along the edges.
  • For digital design, software often gives precise dimensional data, so input these accurately.
  • Record measurements in consistent units to prevent calculation errors. For example, if you measure in inches, ensure all related measurements use the same unit.
Accurate measurements allow precise calculations that affect materials estimation, financial budgeting, and proper spatial management.

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Most popular questions from this chapter

Solve the given problems. A rectangular security area is enclosed on one side by a wall, and the other sides are fenced. The length of the wall is twice the width of the area. The total cost of building the wall and fence is 13,200 dollar. If the wall costs 50.00 dollar and the fence costs 5.00 dollar/m find the dimensions of the area.

Solve the given problems. If two triangles have the same three angles, can you conclude that the triangles are congruent? Explain why or why not.

Change the given angles to radian measure. $$22.5^{\circ}$$

Find the area of each triangle. Equilateral triangle of sides 3200 yd

Solve the given problems. The two sections of a folding door, hinged in the middle, are at right angles. If each section is \(2.5 \mathrm{ft}\) wide, how far are the hinges from the far edge of the other section?
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