Question

find the length of ( overline{cd} ) in the figure below if ( overline{bd} ) is a perpendicular bisector.*** just type the number and nothing else.

Explanation:

Step1: Set up the equation

Since \(BD\) is a perpendicular bisector of \(AC\), \(AD = CD\). So, \(5x - 20=2x + 4\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(5x-2x - 20=2x-2x + 4\), which simplifies to \(3x-20 = 4\).
Add \(20\) to both sides: \(3x-20 + 20=4 + 20\), so \(3x=24\).
Divide both sides by \(3\): \(x=\frac{24}{3}=8\).

Step3: Find the length of \(CD\)

Substitute \(x = 8\) into the expression for \(CD\) (\(2x + 4\)): \(2\times8+4=16 + 4=20\).

Answer:

20