PLZ HELP ASAP LAST SIMMILAR AND CONGRUENT TRIANGLES

Since Y is the right angle of the triangle LNT, LT is the hypotenuse of that triangle. We are going to use the Pythagorean equation to find the measure of LT:
[tex]LT= \sqrt{LY^2+TY^2} [/tex]
[tex]LT= \sqrt{5.2^2+3.9^2} [/tex]
[tex]LT=6.5[/tex]

We can infer from our picture that triangles LNT and YNT are similar. And remember that in similar triangles the corresponding sides are proportional, so we can establish a proportion between sides LT and NT, and between sides  LY and TY:
[tex] \frac{LT}{NT} = \frac{LY}{TY} [/tex]
[tex] \frac{6.5}{NT} = \frac{5.2}{3.9} [/tex]
Solving for NT:
[tex]NT= \frac{(6.5)(3.9)}{(5.2)} [/tex]
[tex]NT=4.88[/tex]

Now the perimeter of our rectangle LINT will be 2LT + 2NT. 
[tex]2(LT)+2(NT)=2(6.5)+2(4.88)=22.76[/tex]

We can conclude that the perimeter of the rectangle LINT is 22.76 units