What is the value of x 5,2.5,7.5,10

This question is referred to two similar triangles.

One triangle has sides x and x - 2.

The other triangle has the respective sides x + x + 5 and x - 2 + x + 1

Then you can state a proportionality relation between the sides>

[x + x + 5] / x = [x - 2 + x + 1] / [x - 2]

=> [2x + 5] / x = [2x - 1] / [x - 2]

=> (2x + 5) (x - 2) = (2x - 1) x

=> 2x^2 - 4x + 5x - 10 = 2x^2 - x

=> x - 10 = - x

=> 2x = 10

=> x = 10 / 2

=> x = 5

Answer: x = 5