From the diagram given in the question, we are asked to find the missing length indicated.
We can see from the diagram that the right triangles are similar, so the ratio of hypotenuse to short leg is the same for all.
So,
x/900 = (1600 + 900)/x
Let's cross multiply:
x² = 900(2500)
let's take square of both sides:
x = √(900) * √(2500)
x = 30(50)
x = 30 * 50
x = 1500
Therefore, the missing length is 1500
