The areas of two similar triangles are 50 dm2 and 32 dm2, the sum of their perimeters

The areas of two similar triangles are 50 dm2 and 32 dm2, the sum of their perimeters is 117 dm. What is the perimeter of the larger triangle?

Let k be the coefficient of similarity of triangles. It is known that S (1) / S (2) = k ^, then
k = root (S (1) / S (2)) = root (50/32) = root (25/16) = 5/4 = 1.25
It is known that P (1) / P (2) = k, that is, P (1) = P (2) * k = 1.25 * P (2).
By the condition of the problem
P (1) + P (2) = 117
1.25 * P (2) + P (2) = 117
P (2) = 117 / 2.25 = 52 dm.
P (1) = 117 – 52 = 65 dm.
Answer: 52 dm; 64 dm.