Chapter 8.4, Problem 31IP

To determine

what is the value of x in the length of hexagon $(x-1.2)cm$ .

Answer to Problem 31IP

  $4.6$

Explanation of Solution

Given:

  

The perimeter of hexagon is $20.4cm$ and the length of hexagon is $(x-1.2)cm$ .

Concept Used:

Perimeter of hexagon is $6a$

Distributive property:

Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the value of x , first the perimeter of hexagon is $6a$ where a represents the length of hexagon, that is $(x-1.2)cm$ , so the equation is as shown below:

  $6\left(x-1.2\right)=20.4$

Now, to solving the equation first using distributive property on left side of the equation and then isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on left side, first add 7.2 both sides and then divide both sides by 6 and then simplify further as shown below,

  $\begin{array}{l}6\left(x-1.2\right)=20.4\\ 6\cdot x-6\cdot 1.2=20.4\\ 6x-7.2=20.4\\ 6x-7.2+7.2=20.4+7.2\\ 6x=27.6\\ \frac{6x}{6}=\frac{27.6}{6}\\ x=4.6\end{array}$

So, the value of x is 4.6 .