Raji draws a square with a side length of x+5
cm. Ava draws a regular hexagon with a side length of x−1
cm. The two figures have the same perimeter. Write an equation that allows you to solve for x
. What is the value of x
?(1 point)
Responses
18
18
13
13
26
26
12
12
The equation that allows you to solve for x is:
4(x+5) = 6(x-1)
To simplify and solve for x, you can expand the expressions:
4x + 20 = 6x - 6
Then, subtract 4x from both sides:
20 = 2x - 6
Next, add 6 to both sides:
26 = 2x
Finally, divide both sides by 2 to solve for x:
x = 13
So, the value of x is 13.
To solve for x, we can set up an equation that equates the perimeters of the square and the regular hexagon.
The perimeter of a square is given by the formula P = 4s, where s is the length of a side.
The perimeter of a regular hexagon is given by the formula P = 6s, where s is the length of a side.
In this case, the side length of the square is x + 5 cm, and the side length of the hexagon is x - 1 cm.
Therefore, the equation is:
4(x + 5) = 6(x - 1)
To solve for x, we can simplify the equation:
4x + 20 = 6x - 6
Rearranging the equation:
6x - 4x = 20 + 6
2x = 26
Dividing both sides of the equation by 2:
x = 13
So, the value of x is 13.