*the figure is shown in the attachment
Answer/Step-by-step explanation:
Since <XYZ and <YZX are said to be congruent, therefore, the side opposite to each of the angle are also equal. Therefore, ∆XYZ is an isosceles ∆.
Find the value of n by creating an equation to solve for n:
XY = (9n + 12) ft
XZ = (15n - 6) ft
XY = XZ (2 equal lengths of isosceles ∆)
9n + 12 = 15n - 6 (substitution)
Combine like terms
9n - 15n = - 12 - 6
-6n = -18
Divide both sides by -6
-6n/-6 = -18/-6
n = 3
Find the length of leg XY by substituting n = 3 into XY = (9n + 12) ft.
XY = (9(3) + 12) ft
XY = (27 + 12) ft
XY = 39 ft
Find the length of leg XZ by substituting n = 3 into XZ = (15n - 6) ft.
XZ = (15(3) - 6) ft
XZ = (45 - 6) ft
XZ = 39 ft
