Question

1. △cde is an isosceles triangle with cd ≅ de. if cd = 9x - 25, de = 6x + 8, and ce = 10x - 73, find the value of x and the measure of each side.

Explanation:

Step1: Set up the equation

Since \(CD\cong DE\), we have \(9x - 25=6x + 8\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(9x-6x - 25=6x-6x + 8\), which simplifies to \(3x-25 = 8\).
Add \(25\) to both sides: \(3x-25 + 25=8 + 25\), so \(3x=33\).
Divide both sides by \(3\): \(x=\frac{33}{3}=11\).

Step3: Find the length of \(CD\) and \(DE\)

Substitute \(x = 11\) into \(CD = 9x-25\): \(CD=9\times11-25=99 - 25=74\).
Since \(CD\cong DE\), \(DE = 74\).

Step4: Find the length of \(CE\)

Substitute \(x = 11\) into \(CE=10x - 73\): \(CE=10\times11-73=110-73 = 37\).

Answer:

\(x = 11\), \(CD=74\), \(DE = 74\), \(CE=37\)