Q:

The ratio of the surface areas of two similar solids is 16:144 what is the ratio of their corresponding side lengths

Accepted Solution

A:
Answer:The ratio of their corresponding side lengths is equal to [tex]\frac{1}{3}[/tex]Step-by-step explanation:step 1Find the scale factorwe know thatIf two figures are similar, then the ratio of its surface areas is equal to the scale factor squaredLetz-------> the scale factorx----> the area of the smaller solidy----> the area of the larger solidso[tex]z^{2}=\frac{x}{y}[/tex]In this problem we have[tex]\frac{x}{y} =\frac{16}{144}[/tex]substitute[tex]z^{2}=\frac{16}{144}[/tex]square root both sides[tex]z=\frac{4}{12}[/tex] ------> scale factorSimplify[tex]z=\frac{1}{3}[/tex]step 2Find the ratio of their corresponding side lengthswe know thatIf two figures are similar, then the ratio of its corresponding sides is equal to the scale factor In this problem we have that the scale factor is equal to [tex]\frac{1}{3}[/tex]thereforeThe ratio of their corresponding side lengths is equal to [tex]\frac{1}{3}[/tex]