Answer:
The perimeter of triangle MNP is 130 units
Explanation:
By the mid segment theorem, we have it that the a side of the smaller inner triangle is 1/2 the measure of the parallel side of the bigger triangle that faces it
This mean RS is half MN, QS is half NP and QR is half MP
Using this, we have it that;
2(x + 4) = 5x - 34
2x + 8 = 5x -34
5x-2x = 34 + 8
3x = 42
x = 42/3
x = 14
So we have RS which is x + 4 as 14 + 4 = 18
The perimeter of the smaller triangle is the sum of its side lengths
We have this as;
22 + 25 + 18 = 65
Furthermore, by the mid segment theorem , the perimeter of the bigger triangle is twice that of the smaller
thus, we have the perimeter of MNP as 2(65) = 130 units