Chapter 7.3, Problem 13IP

To determine

Write and simplify a linear expression of the perimeter of the figure. Find the perimeter when x = 0.8

Answer to Problem 13IP

The Perimeter of the rectangle is $18x$ in, perimeter = 14.4 in when x = 0.8

Explanation of Solution

Given:

The sides of the Rectangle are: $\text{Length}=(5x+1)\text{in}\text{;}\text{Height}\text{=}\text{(}4x-\text{1) in}$

Concept Used:

To add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same.

To subtract two or more monomials that are like terms, subtract the coefficients; keep the variables and exponents on the variables the same. on the variables the same.

Addition of Algebraic expression

In addition of algebraic expressions while adding algebraic expressions we collect the like terms and add them. The sum of several like terms is the like term whose coefficient is the sum of the coefficients of these like terms.

Example:

1. Add: 6a + 8b, 2b - 4a

Solution: 

(6a + 8b) + (2b - 4a) = 6a + 8b + 2b - 4a

Arrange the like terms together, then add. Thus, the required addition

= 6a - 4a + 8b + 2b = 2a + 10b

Calculation:

To add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same.

Perimeter of the Rectangle is = 2 (length + height)

The sides of the Rectangle are: $\text{Length}=(5x+1)\text{in}\text{;}\text{Height}\text{=}\text{(}4x-\text{1) in}$

Now find the perimeter of the rectangle:

Add the like terms and the numbers separately.

  $\begin{array}{l}\text{Perimeter}:\\ 2[(5x+1)+(4x-1)]\\ 2[5x+1+4x-1]\\ 2[5x+4x+1-1]\\ 2(9x)=18x\end{array}$ Perimeter of the rectangle is $18x$ in Find the perimeter of the figure if x = 0.8

Now substitute x = 0.8 in the expression of Perimeter.

The Perimeter of the Rectangle is $18x$ in

  $18x\text{in}=18·0.8=14.4\text{in}$

Thus, The Perimeter of the Rectangle is $18x$ in, the perimeter is 14.4 in when x = 0.8