Short Answer 
The area ratio of two similar triangles with a perimeter ratio of 4:3 is 16:9. Given a total area of 130 cm², the area of the larger triangle is calculated to be 83.2 cm², while the area of the smaller triangle is 46.8 cm².
Step 1: Understanding the Ratio of Areas
The two triangles are similar, which allows us to express their areas in a ratio derived from the square of their perimeter ratio. Given a perimeter ratio of 4:3, the area ratio will be calculated as follows:
- The square of 4 is 16.
- The square of 3 is 9.
- Thus, the area ratio of the triangles becomes 16:9.
Step 2: Calculating Individual Areas Using the Total Area
The total area of both triangles combined is 130 cm². To find the areas of each triangle, use the area ratio derived earlier:
- The formula for the area of the larger triangle becomes: Area of larger triangle = Total Area √ó (16 / (16 + 9)).
- This simplifies to Area of larger triangle = 130 √ó (16 / 25).
- Calculating this gives the area of the larger triangle as 83.2 cm².
Step 3: Finding the Area of the Smaller Triangle
Now, to determine the area of the smaller triangle, use the remainder of the total area:
- The area of the smaller triangle follows the formula: Area of smaller triangle = Total Area √ó (9 / (16 + 9)).
- Simplifying this, we get Area of smaller triangle = 130 √ó (9 / 25).
- This results in the area of the smaller triangle being 46.8 cm².