Question

The street sign shown is a regular hexagon with side lengths of (7.6x+10.4) centimeters. The perimeter of the sign is 737.28 centimeters. Write an equation

Answer 1

The equation for the regular hexagon shown can be represented as 6(7.6x + 10.4) = 737.28

How to represent the perimeter ?

To write an equation for the perimeter of the hexagonal street sign, you need to add up the lengths of all six sides of the hexagon, and set this sum equal to the given perimeter of 737.28 centimeters.

The side length of the hexagon is given as (7.6x + 10.4) centimeters, and there are six sides. So, the perimeter equation can be written as:

6(7.6x + 10.4) = 737.28

Solving for x gives:

6(7.6x + 10.4) = 737.28

45.6x + 62.4 = 737.28

45.6x = 737.28 - 62.4

45.6x = 674.88

x = 674.88 / 45.6

x = 14.82

In conclusion, the equation for the perimeter of the hexagon would be 6(7.6x + 10.4) = 737.28.

Answer 2

Equation:

`6(7.6x+10.4)=737.28`

Solution:

`x=14.8\ centimeters`

Explanation:

Perimeter of a hexagon

We are given the length of the side of a regular hexagon

`l=7.6x+10.4\ centimeters`

And we also know the perimeter of the hexagon is

`P=737.28\ centimeters`

The perimeter of a regular hexagon is 6 times its side, so

`P=6l=6(7.6x+10.4)`

The equation that will give the relation to solve for x is

`6(7.6x+10.4)=737.28`

Reducing

`7.6x+10.4=122.88`

`7.6x=122.88-10.4=112.48`

`\displaystyle x=(112.48)/(7.6)`

`x=14.8\ centimeters`