Answer:
22.75
Step-by-step explanation:
To find the perimeter, first find LT. You can do this using the Pythagorean Theorem to say LT is the square root of LY^2 + YT^2
LT = √(LY^2 + yt^2)
LT = √(5.2^2 + 3.9^2)
LT = √ (27.04 + 15.21)
LT = √ (42.25)
LT = 6.5
Now you know LT is 6.5, and IN is also 6.5 by the definition of a rectangle.
Next find TN.
You can say triangle LYT is similar to triangle TYN. Knowing this, you can set up proportions for corresponding sides.
LY/YT = YT/YN
5.2/3.9 = 3.9/YN
Solve for YN
5.2*YN = 3.9*3.9 Cross multiply
5.2YN = 15.21
YN = 2.925 Divide both sides by 5.2
Now you have YN and YT, so you can use the Pythagorean theorem to find TN
= YN^2 + YT^2
TN = √(2.925^2 + 3.9^2)
TN = √(8.555625+15.21)
TN = √(23.765625)
TN = 4.875
After you have LT and TN, you can find the perimeter using the formula:
P = 2(L) + 2(W)
P = 2(6.5) + 2(4.875)
P = 13 + 9.75
P = 22.75
That was a lot, hope this helps!
