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Chapter 9: Problem 7

Find the perimeter of each rectangle. $$ 5 \mathrm{ft} \text { by } 10 \mathrm{ft} $$

Short Answer

Expert verified
The perimeter is 30 feet.

Step by step solution

01

- Understand the formula for perimeter of a rectangle

The perimeter (P) of a rectangle is calculated using the formula: \[ P = 2 \times ( \text{length} + \text{width} ) \] where length and width are the dimensions of the rectangle.
02

- Identify the dimensions

In this problem, the length (L) is 10 feet, and the width (W) is 5 feet.
03

- Substitute the dimensions into the formula

Using the formula for the perimeter: \[ P = 2 \times (L + W) \] Substitute L = 10 ft and W = 5 ft: \[ P = 2 \times (10 + 5) \]
04

- Calculate the perimeter

Add the length and the width first: \[ 10 + 5 = 15 \] Then multiply by 2: \[ P = 2 \times 15 = 30 \]
05

- State the final answer

The perimeter of the rectangle is 30 feet.

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Key Concepts

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

Geometry and Rectangles Explained
In geometry, a rectangle is a four-sided shape where every angle is a right angle (90 degrees). Opposite sides of a rectangle are equal in length. This makes it easier to calculate their perimeter. The perimeter is simply the total length around the rectangle. To find it, you add up the lengths of all four sides.

A useful property is that the lengths of the opposite sides are the same. So, you can use a formula to find the perimeter quickly without adding each side individually.
Mathematical Formulas for Perimeter
Formulas are like recipes in math. For a rectangle, the formula to find the perimeter is: \( P = 2 \times ( \text{length} + \text{width} ) \). This formula combines the lengths of both pairs of sides.

First, you take the length and the width of the rectangle. After that, you add them together. Finally, you multiply the result by 2. This gives you the sum of all four sides, or the perimeter.

For example, if you have a rectangle that is 10 feet long and 5 feet wide, you substitute those numbers into the formula: \( P = 2 \times (10 + 5) \). Calculate the sum: \( 10 + 5 = 15 \). Then, multiply by 2: \( 2 \times 15 = 30 \). The perimeter is 30 feet.
Measurement in Geometry
Measurement is an important part of geometry. It involves finding dimensions like length, width, and height. Each unit of measure must be the same, like feet, meters, or inches. When solving for the perimeter, make sure all dimensions are in the same unit.

For example, if you want to measure a rectangle's sides and the provided lengths are 10 feet and 5 feet, you should ensure both are in feet before applying the formula. It helps keep calculations accurate and easy to understand.

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