In quadrilateral FGKJ

Question

, FK¯¯¯¯¯¯¯¯
is a perpendicular bisector of GJ¯¯¯¯¯¯¯
. The length of segment GF¯¯¯¯¯¯¯¯
is 6+x
units, and the length of segment JF¯¯¯¯¯¯¯
is 3x−5
units. What is the value of x?

(1 point)

Answer 1

Since \( FK \) is the perpendicular bisector of \( GJ \), it divides \( GJ \) into two equal segments. Therefore, we can set the lengths of segments \( GF \) and \( JF \) equal to each other:

\[ GF = JF \]

Given that:

\[ GF = 6 + x \] \[ JF = 3x - 5 \]

Setting the equations equal gives us:

\[ 6 + x = 3x - 5 \]

Now, we'll solve for \( x \):

1. Subtract \( x \) from both sides:

\[ 6 = 2x - 5 \]

2. Add \( 5 \) to both sides:

\[ 6 + 5 = 2x \] \[ 11 = 2x \]

3. Divide both sides by \( 2 \):

\[ x = \frac{11}{2} = 5.5 \]

Thus, the value of \( x \) is

\[ \boxed{5.5} \]