Question

PLZ HELP ASAP LAST SIMMILAR AND CONGRUENT TRIANGLES

Answer 1

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:
$LT= \sqrt{LY^2+TY^2}$
$LT= \sqrt{5.2^2+3.9^2}$
$LT=6.5$

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:
$\frac{LT}{NT} = \frac{LY}{TY}$
$\frac{6.5}{NT} = \frac{5.2}{3.9}$
Solving for NT:
$NT= \frac{(6.5)(3.9)}{(5.2)}$
$NT=4.88$

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

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