Two triangles are similar, and the ratio of each pair of corresponding sides is 7:3. What is the ratio of the perimeters? What is the ratio of the areas?
since perimeter is a linear measurement the ratio would be 7:3 , but
the ratio of their areas is 7^2 : 3^2 = 49 : 9
49:90
81:256
To find the ratio of the perimeters, we need to compare the lengths of the corresponding sides of the two triangles. Since the ratio of each pair of corresponding sides is 7:3, we can say that the ratio of the perimeters is also 7:3.
Let's assume the lengths of the corresponding sides of the first triangle are 7x and 3x, and the lengths of the corresponding sides of the second triangle are 7y and 3y, where x and y are constants.
The ratio of the perimeters will be (7x + 7y) : (3x + 3y), which simplifies to 7x/3x, or simply, 7/3.
Therefore, the ratio of the perimeters is 7:3.
To find the ratio of the areas, we need to compare the squares of the lengths of the corresponding sides. Since the sides of similar triangles are proportional, the ratio of their areas will be the square of the ratio of their corresponding sides.
In this case, the sides have a ratio of 7:3, so the ratio of their areas will be (7/3)^2, which simplifies to 49/9.
Therefore, the ratio of the areas is 49:9.