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?
The perimeter of Raji's square is given by 4 * (x + 5) = 4x + 20.
The perimeter of Ava's hexagon is given by 6 * (x - 1) = 6x - 6.
To find the value of x, we set the two perimeters equal to each other:
4x + 20 = 6x - 6
Subtract 4x from both sides:
20 = 2x - 6
Add 6 to both sides:
26 = 2x
Divide both sides by 2:
x = 13
Therefore, the value of x is 13.
To write an equation that allows us to solve for x, we need to equate the perimeters of the square and the regular hexagon.
The perimeter of a square is given by P_square = 4 * side length.
Therefore, the perimeter of the square drawn by Raji is P_square = 4(x+5) cm.
The perimeter of a regular hexagon is given by P_hexagon = 6 * side length.
Therefore, the perimeter of the hexagon drawn by Ava is P_hexagon = 6(x-1) cm.
We can equate the two perimeters and solve for x:
4(x+5) = 6(x-1)
Now, let's solve for x:
4x + 20 = 6x - 6
20 + 6 = 6x - 4x
26 = 2x
x = 13
Therefore, the value of x is 13.