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 a square is given by 4 times its side length, so the perimeter of Raji's square is 4(x+5) cm.
The perimeter of a regular hexagon is given by 6 times its side length, so the perimeter of Ava's hexagon is 6(x-1) cm.
Since the two figures have the same perimeter, we can set up the equation: 4(x+5) = 6(x-1).
Expanding and simplifying the equation gives us: 4x+20 = 6x-6.
Subtracting 4x and adding 6 to both sides of the equation, we get: 26 = 2x.
Dividing both sides of the equation by 2, we find that: x = 13.
Therefore, the value of x is 13.
To write an equation that allows us to solve for x, we need to set the perimeters of the square and the hexagon equal to each other.
The perimeter of a square is given by P = 4s, where s is the side length.
So, the perimeter of the square drawn by Raji is 4(x+5) = 4x + 20.
The perimeter of a regular hexagon is given by P = 6s, where s is the side length.
So, the perimeter of the hexagon drawn by Ava is 6(x-1) = 6x - 6.
Setting these two expressions equal to each other gives us the equation:
4x + 20 = 6x - 6.
Now, we can solve for x:
2x + 20 = -6,
2x = -6 - 20,
2x = -26,
x = -26/2,
x = -13.
Therefore, the value of x is -13.