Solve for x, given that BD = 40, FD = 2x - 2, and F is the midpoint of BD.

Understand the Problem

The problem gives us a diagram of a quadrilateral with intersecting diagonals. We're given that the length of diagonal BD is 40, and the length of FD is 2x - 2. We need to find the value of x, assuming that F is the midpoint of BD.

Answer

D) 11

Steps to Solve

Use the midpoint information

Since F is the midpoint of BD, we know that FD is half the length of BD.

Set up the equation

We can write this relationship as: $FD = \frac{1}{2}BD$

Substitute the given values

Substitute $BD = 40$ and $FD = 2x - 2$ into the equation:

$2x - 2 = \frac{1}{2}(40)$

Simplify the equation

Simplify the right side of the equation:

$2x - 2 = 20$

Solve for x

Add 2 to both sides of the equation:

$2x = 22$

Divide both sides by 2:

$x = 11$

D) 11

More Information

The midpoint divides a line segment into two equal parts.

Tips

A common mistake is to set FD equal to BD instead of half of BD. Remember to use the information about F being the midpoint correctly.

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