Sure, let's solve the problem step by step.
We are given the lengths of the sides of a hexagon and told that the perimeter of the hexagon is 1.44 cm. We need to find the value of [tex]\( x \)[/tex].
The lengths of the sides of the hexagon are:
1. [tex]\(x - 5\)[/tex]
2. [tex]\(2x\)[/tex]
3. [tex]\(2x\)[/tex]
4. [tex]\(2x + 7\)[/tex]
5. [tex]\(2x - 1\)[/tex]
Let's assume the sixth side is also [tex]\(x - 5\)[/tex] for simplicity, since we're given only five sides but a hexagon has six sides.
First, let's add up the lengths of all the sides to find the perimeter:
[tex]\[
(x - 5) + 2(2x) + (2x + 7) + (2x - 1) + (x - 5)
\][/tex]
Simplifying this expression:
[tex]\[
(x - 5) + 2x + 2x + (2x + 7) + (2x - 1) + (x - 5)
\][/tex]
Combine like terms:
[tex]\[
x - 5 + 2x + 2x + 2x + 7 + 2x - 1 + x - 5
\][/tex]
Combine all the [tex]\(x\)[/tex] terms:
[tex]\[
x + 2x + 2x + 2x + 2x + x = 10x
\][/tex]
Combine all the constant terms:
[tex]\[
-5 + 7 - 1 - 5 = -4
\][/tex]
So the sum of the side lengths is:
[tex]\[
10x - 4
\][/tex]
We are given that the perimeter is 1.44 cm, so:
[tex]\[
10x - 4 = 1.44
\][/tex]
Now, solve for [tex]\(x\)[/tex]:
First, add 4 to both sides of the equation:
[tex]\[
10x = 1.44 + 4
\][/tex]
[tex]\[
10x = 5.44
\][/tex]
Now, divide both sides by 10:
[tex]\[
x = \frac{5.44}{10}
\][/tex]
[tex]\[
x = 0.544
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(0.544\)[/tex].
