Chapter 7.3, Problem 5GP

(a)

To determine

Write and simplify a linear expression of the perimeter of the figure.

Answer to Problem 5GP

Perimeter of the figure is $6x+4$

Explanation of Solution

Given:

The sides of the figure are: $x,x+2,2x,2x+2$

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.

The sides of the figure are: $x,x+2,2x,2x+2$

Perimeter of the figure is the sum of all sides.

Perimeter: $x+x+2+2x+2x+2$

Add the like terms and the numbers separately.

  $\begin{array}{l}x+x+2+2x+2x+2\\ (x+x+2x+2x)+(2+2)\\ 6x+4\end{array}$ Perimeter of the figure is $6x+4$

Thus, the perimeter of the figure is $6x+4$

(b)

To determine

Find the perimeter of the figure if x = 4

Answer to Problem 5GP

The value of the perimeter is 28.

Explanation of Solution

Given:

Perimeter of the figure is $6x+4$

Concept Used:

Now substitute x = 4 in the expression of Perimeter.

Perimeter of the figure is $6x+4$

Calculation:

Now substitute x = 4 in the expression of Perimeter.

Perimeter of the figure is $6x+4$

  $\begin{array}{l}6x+4\\ 6·4+4=24+4=28\\ 6x+4=28\end{array}$

Thus, the value of the perimeter is 28