Question

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

Answer 1

Answer:

4:12

Step-by-step explanation: apex

Answer 2

Answer:

The ratio of their corresponding side lengths is equal to $\frac{1}{3}$

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-------> the scale factor

x----> the area of the smaller solid

y----> the area of the larger solid

so

$z^{2}=\frac{x}{y}$

In this problem we have

$\frac{x}{y} =\frac{16}{144}$

substitute

$z^{2}=\frac{16}{144}$

square root both sides

$z=\frac{4}{12}$ ------> scale factor

Simplify

$z=\frac{1}{3}$

step 2

Find the ratio of their corresponding side lengths

we know that

If 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 $\frac{1}{3}$

therefore

The ratio of their corresponding side lengths is equal to $\frac{1}{3}$