What is the value of x?

You have a right triangle with an altitude to the hypotenuse. The second mean proportional theorem says that a leg is the geometric mean of its projection onto the hypotenuse and the hypotenuse.
(x+11)^2=x(x+23)
x^2+22x+121=x^2+23x
x=121

if you have more maths question use mathqu homework support app in app store this is the best app to get answers from live tutors who write step by step maths answers search for mathqu in app store

You have a right triangle with an altitude to the hypotenuse. The second mean proportional theorem says that a leg is the geometric mean of its projection onto the hypotenuse and the hypotenuse.

(x+11)^2=x(x+23)
x^2+22x+121=x^2+23x
x=121

Or if you like similar triangles directly:
adjacent/hypotenuse = adjacent/hypotenuse.