The perimeter of the triangle DGN is 400 cm. It is known that the DN side is 30 cm smaller than the GN side

The perimeter of the triangle DGN is 400 cm. It is known that the DN side is 30 cm smaller than the GN side. What is the length of the segment GN if DG = 17 dm.

1. Let us subtract the length of the side DG from the perimeter of the triangle, we obtain the sum of the sides DN and GN:
400 cm – 17 dm = 40 dm – 17 dm = 23 dm.
2. Subtract from the sum of DN and GN the difference between these sides, we get the doubled value of the side DN:
23 dm – 30 cm = 23 dm – 3 dm = 20 dm.
3. Divide 20 dm by 2, we get the length DN:
20/2 = 10 dm.
4. Find the length GN by adding 30 cm to the length DN:
10 dm + 30 cm = 10 dm + 3 dm = 13 dm.
Answer: GN is 13 dm.