Solve for x, given that ABCD is an isosceles trapezoid, AC = 2x + 12, and BD = 4x - 30.
the diagonals of an isosceles trapezoid are equal
2 x + 12 = 4 x - 30
2 x = 42
x = 21
To solve for x, we need to set up an equation using the given information about the lengths of the trapezoid's sides.
In an isosceles trapezoid, the two non-parallel sides (AC and BD) have equal lengths. Therefore, we can set up the equation AC = BD.
Given that AC = 2x + 12 and BD = 4x - 30, we can write:
2x + 12 = 4x - 30
To solve for x, we will isolate the variable on one side of the equation. Let's begin by moving the terms involving x to one side:
2x - 4x = -30 - 12
Simplifying the equation:
-2x = -42
Next, we will isolate x by dividing both sides of the equation by -2:
(-2x) / (-2) = (-42) / (-2)
This simplifies to:
x = 21
Therefore, the value of x is 21.
To solve for x in this problem, we need to use the properties of an isosceles trapezoid and set up an equation involving the lengths of the sides.
First, let's recall that in an isosceles trapezoid, the non-parallel sides (AC and BD) are equal in length. So, we can set up an equation:
AC = BD
Next, substitute the given values into the equation:
2x + 12 = 4x - 30
Now, we can solve for x. Start by isolating the x term on one side of the equation. In this case, we'll move the 2x term to the right side:
2x - 4x = -30 - 12
Simplifying the equation further:
-2x = -42
Now, divide both sides of the equation by -2 to solve for x:
x = -42 / -2
Simplifying this expression gives us:
x = 21
Therefore, the value of x is 21.