ABCD is a trapezoid. If AC is equal to 8x - 3 and BD is equal to 2x + 9, find the value of x so that ABCD is isosceles.
AC=BD...
Point C is located on the perpendicular bisector of AB.
What is the distance from A to C given the following?
AC = 2x+9
BC = 8x-3
To find the value of x for the trapezoid ABCD to be isosceles, we need to equate the lengths of the non-parallel sides, AC and BD.
AC = 8x - 3
BD = 2x + 9
Since an isosceles trapezoid has two pairs of equal sides, we can set up the equation:
AC = BD
Equating the lengths:
8x - 3 = 2x + 9
To solve for x, we can follow these steps:
1. Move the constant term to the other side of the equation:
8x - 2x = 9 + 3
6x = 12
2. Divide both sides of the equation by 6 to isolate x:
6x/6 = 12/6
x = 2
Therefore, the value of x that makes ABCD an isosceles trapezoid is x = 2.