The diagonals of rhombus FGHJ intersect at point K. If side GH is equal to 3x - 10 and side JH is equal to 6x - 19, find x.
All 4 sides of a rhombus are equal.
GH = 3x-10.
JH = 6x-19.
GH = JH,
3x-10 = 6x-19,
6x-3x = 19-10,
3x = 9,
x = 3.
To find the value of x, we need to use the fact that in a rhombus, the diagonals are perpendicular bisectors of each other. This means that the diagonals intersect at a right angle and divide each other into two equal parts.
Let's start by setting up an equation using this information. We know that the diagonals intersect at point K, so we can use this to find the relationship between the lengths of the sides GH, HJ, GK, and KJ.
Since GK is a bisector of HJ, we can say that GH = GJ and HJ = HK.
Now, let's substitute the given expressions for GH and HJ:
3x - 10 = 6x - 19 (equation for GH = GJ)
6x - 19 = 3x - 10 (equation for HJ = HK)
Now, we can solve these equations to find the value of x:
3x - 10 = 6x - 19
3x - 6x = -19 + 10
-3x = -9
x = (-9)/(-3)
x = 3
So, x = 3. Therefore, we have found the value of x as 3.