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Chapter 1: Problem 49

Find the perimeter of the rectangle having the given length and width. $$ \mathrm{L}=25 \mathrm{in}, \mathrm{W}=16 \mathrm{in} $$

Short Answer

Expert verified
The perimeter of the rectangle is 82 inches.

Step by step solution

01

Understand the Definition of Perimeter for a Rectangle

The perimeter of a rectangle is defined as the total length around the rectangle. It is calculated as the sum of all four sides of the rectangle. For a rectangle, this can be expressed as: \( P = 2L + 2W \), where \( L \) is the length and \( W \) is the width.
02

Substitute the Given Values into the Formula

We substitute \( L = 25 \) in. and \( W = 16 \) in. into the formula. Replace \( L \) and \( W \) in the formula, leading to \( P = 2(25) + 2(16) \).
03

Perform the Multiplications

First, multiply the length by 2: \( 2 \times 25 = 50 \). Then, multiply the width by 2: \( 2 \times 16 = 32 \).
04

Add the Results

Add the results from the previous step to find the perimeter. Combine \( 50 + 32 \) to get \( 82 \).
05

State the Final Answer

The perimeter of the rectangle is \( 82 \) inches. Make sure to include the unit of measurement, which is in inches.

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Key Concepts

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

rectangle geometry
A rectangle is one of the most basic shapes in geometry, recognized by its four sides and four right angles. Each rectangle has two pairs of opposite sides that are equal in length. Unlike a square, the adjacent sides of a rectangle can differ in length. This shape can be easily identified by its corners, all formed at 90-degree angles. For example, a standard sheet of paper is a rectangle.

In rectangles, length and width are interchangeable terms for the longer and shorter sides, respectively. These definitions help set the foundation for calculating important metrics like perimeter and area, which are central to understanding rectangle geometry.
formula for perimeter
To determine the perimeter of a rectangle, we use a specific formula. The perimeter refers to the total distance around the edge of the rectangle. Given a rectangle with length (L) and width (W), the formula for its perimeter (P) is:
  • \( P = 2L + 2W \)
This formula arises from adding the lengths of all four sides. Since opposite sides of a rectangle are equal, we multiply each dimension by 2.

This equation is a fundamental piece of rectangle geometry and is crucial for problems involving dimensions of flat surfaces, fences around rectangular gardens, or borders around paintings. Understanding this formula allows us to compute the perimeter once we know the rectangle's length and width.
calculating perimeter
Let鈥檚 walk through calculating the perimeter of a rectangle using the given values from an example problem. In our scenario, the length (L) is 25 inches, and width (W) is 16 inches.

**Step-by-Step Calculation**:
  • First, apply the formula: \( P = 2L + 2W \).
  • Then, substitute the known values of length and width: \( P = 2(25) + 2(16) \).
  • Performing the calculations, multiply the length by 2 to get 50, and the width by 2 to get 32.
  • Finally, add these two amounts (50 + 32) to find the perimeter: \( P = 82 \).
  • Always remember to label the final answer with appropriate units, here it鈥檚 82 inches.
This step-by-step process helps in avoiding errors and ensures each calculation is done precisely, leading to an accurate perimeter.

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Most popular questions from this chapter

This exercise introduces the Sieve of Eratosthenes, an ancient algorithm for finding the primes less than a certain number \(n\), first created by the Greek mathematician Eratosthenes. Consider the grid of integers from 2 through 100 . $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hline 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 \\ \hline 22 & 23 & 24 & 25 & 26 & 27 & 28 & 29 & 30 & 31 \\ \hline 32 & 33 & 34 & 35 & 36 & 37 & 38 & 39 & 40 & 41 \\ \hline 42 & 43 & 44 & 45 & 46 & 47 & 48 & 49 & 50 & 51 \\ \hline 52 & 53 & 54 & 55 & 56 & 57 & 58 & 59 & 60 & 61 \\ \hline 62 & 63 & 64 & 65 & 66 & 67 & 68 & 69 & 70 & 71 \\ \hline 72 & 73 & 74 & 75 & 76 & 77 & 78 & 79 & 80 & 81 \\ \hline 82 & 83 & 84 & 85 & 86 & 87 & 88 & 89 & 90 & 91 \\ \hline 92 & 93 & 94 & 95 & 96 & 97 & 98 & 99 & 100 & \\ \hline \end{array} $$ To find the primes less than 100 , proceed as follows. i) Strike out all multiples of \(2(4,6,8\), etc. \()\) ii) The list's next number that has not been struck out is a prime number. iii) Strike out from the list all multiples of the number you identified in step (ii). iv) Repeat steps (ii) and (iii) until you can no longer strike any more multiples. v) All unstruck numbers in the list are primes.

Simplify the given expression. $$ \frac{13+35}{3(4)} $$

Simplify the given expression. $$ 10+11\left[20-\left(2^{2}+1\right)\right] $$

Simplify the given expression. $$ 7 \cdot[8-5]-10 $$

Simplify the given expression. $$ 14 \cdot 18+9 \div 3-7 \cdot 13 $$
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