Question

drag each label to the correct location on the table. not all labels will be used. the perimeter of base abcd is 30 inches, and the perimeter of base stuv is 20 inches. complete the table with the ratios of the heights, surface areas, and volumes of these two similar rectangular prisms. assume the ratios are written in the form figure 1 : figure 2. figure 1 figure 2 ratio of heights ratio of surface areas ratio of volumes

Explanation:

Step1: Recall similar - solid properties

For two similar rectangular prisms, if the ratio of the perimeters of their bases is \(a:b\), the ratio of their corresponding linear dimensions (such as height) is the same as the ratio of the perimeters of their bases. Given the perimeter of base \(ABCD\) is \(30\) inches and the perimeter of base \(STUV\) is \(20\) inches, the ratio of the perimeters of the bases is \(\frac{30}{20}=\frac{3}{2}\). So the ratio of heights is \(\frac{3}{2}\).

Step2: Calculate ratio of surface areas

For two similar solids, if the ratio of their corresponding linear dimensions is \(k\), the ratio of their surface areas is \(k^{2}\). Since \(k = \frac{3}{2}\), the ratio of the surface areas is \(k^{2}=(\frac{3}{2})^{2}=\frac{9}{4}\).

Step3: Calculate ratio of volumes

For two similar solids, if the ratio of their corresponding linear dimensions is \(k\), the ratio of their volumes is \(k^{3}\). Since \(k=\frac{3}{2}\), the ratio of the volumes is \(k^{3}=(\frac{3}{2})^{3}=\frac{27}{8}\).

Answer:

Ratio of Heights	Ratio of Surface Areas	Ratio of Volumes