Final answer:
By setting up a proportion based on the provided ratio of the perimeters and solving for the original perimeter, we find that the perimeter of the given triangle is 120 cm.
Step-by-step explanation:
The student is tasked with solving a ratio problem related to the perimeters of triangles in mathematics. We are given that each side of a triangle is increased by 10 cm and the ratio of the perimeters of the new triangle to the given triangle is 5:4. This means for every 4 units of perimeter in the original triangle, the new triangle's perimeter is 5 units.
Let's denote the perimeter of the original triangle as P. When we increase each side by 10 cm, since a triangle has three sides, we are adding a total of 30 cm to the perimeter.
The new perimeter thus becomes P + 30 cm.
The ratio of the new perimeter to the old perimeter is given by (P + 30)/P = 5/4.
To find the original perimeter (P), we can set up and solve the proportion:
(P + 30)/P = 5/4
We cross multiply to solve for P:
4(P + 30) = 5P
4P + 120 = 5P
120 = 5P - 4P
120 = P
Therefore, the perimeter of the given triangle is 120 cm.