Question

1. xz = n, wz = 2n - 5, and the perimeter of △xwz is 20. what is the value of n? 3 7 5 6

Explanation:

Step1: Determine the relationship between sides

Since \( \triangle XWZ\) is isosceles (\(WX = WZ\) as indicated by the marks), perimeter \(P=XZ + WX+WZ\). Given \(XZ = n\), \(WZ = 2n - 5\), and \(WX = WZ=2n - 5\).

Step2: Set up the perimeter equation

\(P=n+(2n - 5)+(2n - 5)\). Substitute \(P = 20\):

$$
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Step3: Solve for \(n\)

Add \(10\) to both sides: \(5n=20 + 10=30\). Divide both sides by \(5\): \(n=\frac{30}{5}=6\)

Answer:

\(6\) (the fourth option)