In quadrilateral FGKJ , 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?

Answer 1

To find the value of \( x \) in quadrilateral \( FGKJ \), we start with the information provided about the segments. Since \( FK \) is the perpendicular bisector of \( GJ \), it implies that the point \( F \) is equidistant from points \( G \) and \( J \).

Given that the lengths of the segments are:

• \( GF = 6 + x \)
• \( JF = 3x - 5 \)

We can set these two expressions equal to each other because \( F \) is equidistant from \( G \) and \( J \):

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

Next, we will solve for \( x \).

1. Start by isolating \( x \): \[ 6 + x + 5 = 3x \] \[ 11 + x = 3x \]

2. Rearranging gives: \[ 11 = 3x - x \] \[ 11 = 2x \]

3. Divide both sides by 2: \[ x = \frac{11}{2} \]

Thus, the value of \( x \) is:

\[ \boxed{\frac{11}{2}} \]

Answer 2

what is the value of x