The area of the larger triangle is 83.2 and the smaller triangle is 46.8 square centimeters.
Given
The ratio of the perimeters of two similar triangles is 4:3.
The sum of their areas is 130cm2.
Area of the triangle;
The area of a triangle is the region enclosed within the sides of the triangle.
The ratio of the perimeter is 4:3.
Then the areas are in the following ratio:
[tex]=\dfrac{4^2}{3^2}\\\\=\dfrac{16}{9}[/tex]
The area of the larger triangle is;
[tex]\rm Area \ of \ larger \ triangle=(Sum \ of \ both \ triangles \ area ) \times \dfrac{Ratio \ of \ larger \ triangle}{larger \ triangle + smaller \ triangle}\\\\ Area \ of \ larger \ triangle=(130) \times \dfrac{16}{16+9}\\\\ Area \ of \ larger \ triangle=130\times \dfrac{16}{25}\\\\ Area \ of \ larger \ triangle=130\times 0.64\\\\ Area \ of \ larger \ triangle=83.2[/tex]
The area of the smaller triangle is;
[tex]\rm Area \ of \ larger \ triangle=(Sum \ of \ both \ triangles \ area ) \times \dfrac{Ratio \ of \ larger \ triangle}{larger \ triangle + smaller \ triangle}\\\\ Area \ of \ smaller \ triangle=(130) \times \dfrac{9}{16+9}\\\\ Area \ of \ larger \ triangle=130\times \dfrac{9}{25}\\\\ Area \ of \ larger \ triangle=130\times 0.36\\\\ Area \ of \ larger \ triangle=46.8[/tex]
Hence, the area of the larger triangle is 83.2 and the smaller triangle is 46.8 square centimeters.
To know more about triangles click the link given below.
https://brainly.com/question/16171588
