Given:
The pair of similar triangles.
Base of smaller triangle = 10 in
Base of larger triangle = 14 in
To find:
The ratio of the perimeters and the ratio of the areas.
Solution:
Ratio of perimeter of similar triangles is equal to the ratio of their corresponding sides.
[tex]\text{Ratio of perimeters}=\dfrac{10\ in.}{14\ in.}[/tex]
[tex]\text{Ratio of perimeters}=\dfrac{5}{7}[/tex]
[tex]\text{Ratio of perimeters}=5:7[/tex]
The ratio of area of similar triangles is equal to the ratio of squares of their corresponding sides.
[tex]\text{Ratio of areas}=\dfrac{(10)^2}{(14)^2}[/tex]
[tex]\text{Ratio of areas}=\dfrac{100}{196}[/tex]
[tex]\text{Ratio of areas}=\dfrac{25}{49}[/tex]
[tex]\text{Ratio of areas}=25:49[/tex]
Therefore, the ratio of the perimeters is 5:7 and the ratio of the areas 25:49.