Question

1. find cd.

Explanation:

Step1: Set up the equation

Since \(AB = BC\) (marked with equal - length symbols), \(\triangle ABC\) is isosceles and \(BD\) is the median (\(AD = DC\)). So, \(9x - 15=7x - 1\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(9x-7x - 15=7x - 7x-1\), which gives \(2x-15=-1\).
Add \(15\) to both sides: \(2x-15 + 15=-1 + 15\), so \(2x = 14\).
Divide both sides by \(2\): \(x=\frac{14}{2}=7\).

Step3: Find \(CD\)

Substitute \(x = 7\) into the expression for \(CD\) (\(CD=7x - 1\)). Then \(CD=7\times7-1\).
Calculate \(7\times7-1=49 - 1=48\).

Answer:

\(48\)