Question

applying the converse of the isosceles triangle theorem
consider isosceles △xyz.
what is the value of n?
what is the measure of leg xy? ft
what is the measure of leg xz? ft

Explanation:

Step1: Apply the converse of the isosceles triangle theorem

Since \(\triangle XYZ\) is isosceles and \(\angle Y=\angle Z\), then \(XY = XZ\). So, \(9n + 12=15n-6\).

Step2: Solve the equation for \(n\)

Subtract \(9n\) from both sides: \(12 = 6n-6\).
Add \(6\) to both sides: \(18=6n\).
Divide both sides by \(6\): \(n = 3\).

Step3: Find the length of \(XY\)

Substitute \(n = 3\) into \(9n + 12\): \(9\times3+12=27 + 12=39\).

Step4: Find the length of \(XZ\)

Substitute \(n = 3\) into \(15n-6\): \(15\times3-6=45 - 6=39\).

Answer:

The value of \(n\) is \(3\).
The measure of leg \(XY\) is \(39\) ft.
The measure of leg \(XZ\) is \(39\) ft.