Answer:
n = 3
XY = 39 ft
XZ = 39 ft
Explanation:
If we rotate the triangle 90° to the right we can see that the congruent angles are now on the bottom, making it the "more commonly seen isosceles triangle" we know.
This means that the two legs will be congruent to each other, so we can set them equal and solve for n:
(9n + 12) = (15n - 6)
9n + 12 = 15n - 6
9n + 18 = 15n
18 = 6n
6n = 18
n = 3
Now we can plug this value of n (3) into one of the expressions to solve for the legs. Since they will be the same length we only need to do one, but I will do both to make sure my work is as correct as possible:
XY
9n + 12
9(3) + 12
27 + 12 = 39
XZ
15n - 6
15(3) - 6
45 - 6 = 39
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather