Answer :
Given:
The smallest cube has a edge length of 6 inches.
The ratios of similarity to the smallest cube are 1.25, 43 , 1.5, 74 , and 2 respectively.
To find:
The edge lengths of the other cubes.
Solution:
If two figures are similar, then the ratios of similarity is equal to the ratio of their corresponding sides.
Let the edge of other cube be x.
[tex]\text{Ratio of similarity}=\dfrac{\text{Edge of other cube}}{\text{Edge of smaller cube}}[/tex]
[tex]\text{Ratio of similarity}=\dfrac{x}{6}[/tex]
[tex]6\times \text{Ratio of similarity}=x[/tex]
It means, the edges of other cubes are 6 times of the ratio of similarity to the smallest cube.
Now,
[tex]6(1.25)=7.5[/tex]
[tex]6(\dfrac{4}{3})=8[/tex]
[tex]6(1.5)=9[/tex]
[tex]6(\dfrac{7}{4})=10.5[/tex]
[tex]6(2)=12[/tex]
Therefore, the edges of other cubes are 7.5, 8, 9, 10.5 and 12 respectively.