A table is shaped like a regular hexagon. The length of one side is (3x + 3) in. and the length of another side is (4x − 4) in.. Find the length of a side.
the sides are equal.
3x+3=4x-4
x=7
side= 3*7+3=24
To find the length of a side of the regular hexagon, we need to equate the expressions for the two sides given.
Let the length of one side be (3x + 3) in., and the length of another side be (4x - 4) in.
Since a regular hexagon has six equal sides, we can set up an equation:
3x + 3 = 4x - 4
To isolate x, we rearrange the equation:
3x - 4x = -4 - 3
-x = -7
Multiplying both sides by -1, we get:
x = 7
Now that we have the value of x, we can substitute it back into either expression to find the length of one side.
Let's use the expression (3x + 3):
Length of one side = 3(7) + 3 = 21 + 3 = 24
Therefore, the length of one side of the regular hexagon is 24 inches.
To find the length of a side of the regular hexagon given by (3x + 3) in. and (4x - 4) in., we need to equate these two expressions and solve for x.
Setting the expressions equal to each other:
3x + 3 = 4x - 4
To isolate x, let's move the x term to one side and the constant terms to the other side:
3 + 4 = 4x - 3x - 4
Combine and simplify the terms:
7 = x - 4
Now, let's isolate x by moving the constant term to the other side:
7 + 4 = x
11 = x
Therefore, the value of x is 11.
To find the length of a side, plug in the value of x into either of the expressions:
For (3x + 3):
Length of a side = 3(11) + 3
Length of a side = 33 + 3
Length of a side = 36 inches
Or for (4x - 4):
Length of a side = 4(11) - 4
Length of a side = 44 - 4
Length of a side = 40 inches
So, the length of a side of the regular hexagon is 36 inches or 40 inches, depending on which expression you choose to work with.