Answer:
x=18
Step-by-step explanation:
In this question we can use the Geometric mean of leg theorem
The theorem states that the hypotenuse/leg 2 = leg 2/part 2
In this problem, leg 2 is x+18, the hypotenuse is 72, and part 2 is x.
Plugging the given values in, we get
72/x+18=x+18/x
We can then simplify it.
(x+18)^2=72x
x^2+36x+324=72x
x^2-36x+324=0
That is equal to (x-18)^2
So, x=18
