Question

ft = 2 + x
fd = 4x - 4
find fd

Explanation:

Step1: Use the property of a kite's diagonals

In a kite, one diagonal is bisected by the other. Here, \( FD = 2FT \).

Step2: Set up the equation

Since \( FD = 4x - 4 \) and \( FT=2 + x \), we have \( 4x - 4=2(2 + x) \).

Step3: Solve the equation

Expand the right - hand side: \( 4x - 4 = 4 + 2x \).
Subtract \( 2x \) from both sides: \( 4x-2x - 4=4 + 2x-2x \), which gives \( 2x - 4 = 4 \).
Add \( 4 \) to both sides: \( 2x-4 + 4=4 + 4 \), so \( 2x=8 \).
Divide both sides by \( 2 \): \( x = 4 \).

Step4: Find \( FD \)

Substitute \( x = 4 \) into \( FD = 4x - 4 \). Then \( FD=4\times4 - 4=16 - 4 = 12 \).

Answer:

\( 12 \)