Kate has a kite with the dimensions shown below. what is the value of x?

Hey there! :D

We will use the properties of similar triangles to figure this out. 

We will use two triangles inside the kite, with sides with the value of "x". 

Smaller triangle:

Smaller side= 11

Bottom side= x

Bigger triangle:

Smaller side= x

Bottom side= 25



Cross multiply. 

25*11= 275

x*x= 

Find the square root. 

√275= 16.583.... 

Or 5√11. 

I hope this helps!
~kaikers