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= √(LY^2+TY^2)`

`LT= √(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:

`(LT)/(NT) = (LY)/(TY)`

`(6.5)/(NT) = (5.2)/(3.9)`
Solving for NT:

`NT= ((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