A table is shaped like a regular hexagon. The length of one side is (2x + 2) in. and the length of another side is (3x − 4) in.. Find the length of a side
the lengths of a regular hexagon should all be equal.
So, set (2x + 2)=(3x − 4) and solve for x.
To find the length of a side of the regular hexagon, we need to set up and solve an equation using the given expressions for the lengths of two sides.
Let's assume that "a" represents the length of a side of the hexagon.
According to the given information, one side of the hexagon has a length of (2x + 2) inches, and another side has a length of (3x - 4) inches.
So, we can set up the following equation:
2x + 2 = 3x - 4
To solve for x, we will isolate the x term on one side of the equation by moving the constant term to the other side:
2x - 3x = -4 - 2
-x = -6
To determine the value of x, we need to divide both sides of the equation by -1:
x = -6 / -1
This simplifies to:
x = 6
Now that we have the value of x, we can substitute it back into either of the expressions for the side lengths to find the length of a side:
a = 2x + 2
a = 2(6) + 2
a = 12 + 2
a = 14
Therefore, the length of a side of the regular hexagon is 14 inches.