The areas of corresponding faces of two similar triangular prisms are 49cm squared and 25cm squared. What is the ratio of the corresponding side lengths? Of the perimeters of the corresponding faces? Of the volume?
ratio of corresponding sides
= 7 : 5
since perimeter is a linear measurement, the ratio of perimeter is also
7 : 5
ratio of volumes = 6^3 : 5^3
= 343 : 125
To find the ratio of the corresponding side lengths, you need to take the square root of the ratio of the areas because the areas of similar figures are proportional to the square of the side lengths.
The area of a face of the first prism is 49 cm², and the area of the corresponding face of the second prism is 25 cm². Therefore, the ratio of their areas is 49/25.
To find the ratio of the corresponding side lengths, take the square root of the ratio of the areas:
√(49/25) = 7/5
So, the ratio of the corresponding side lengths is 7:5.
To find the ratio of the perimeters of the corresponding faces, you need to compare the corresponding sides.
Since the ratio of the side lengths is 7:5, the ratio of the perimeters will also be 7:5 because the perimeter is just the sum of all the sides.
Therefore, the ratio of the perimeters of the corresponding faces is also 7:5.
To find the ratio of the volumes of the two prisms, we need to compare their corresponding dimensions. Since the prisms are similar, the ratio of their corresponding side lengths also applies to the height (or length) of the prisms.
So, the ratio of the volume of two similar prisms is given by the cube of the ratio of their corresponding side lengths:
(7/5)³ = 343/125
Therefore, the ratio of the volumes of the two prisms is 343:125.