Answer :
We want to check if the two sides of each option represent the same measurement. Let’s go step by step for each option.
[tex]$\textbf{Option A: }$[/tex]
We compare [tex]$15$[/tex] kilometers with [tex]$1,\!500,\!000$[/tex] centimeters.
Since
[tex]$$1 \text{ km} = 100,\!000 \text{ cm},$$[/tex]
then
[tex]$$15 \text{ km} = 15 \times 100,\!000\,\text{cm} = 1,\!500,\!000\,\text{cm}.$$[/tex]
This shows the two measurements are equal.
[tex]$\textbf{Option B: }$[/tex]
We need to see if [tex]$28$[/tex] feet is equal to [tex]$9$[/tex] yards.
Recall that
[tex]$$1 \text{ yard} = 3 \text{ feet},$$[/tex]
so
[tex]$$28 \text{ ft} = \frac{28}{3} \text{ yards} \approx 9.\overline{3}\text{ yards}.$$[/tex]
Since [tex]$9.\overline{3}$[/tex] yards is not equal to [tex]$9$[/tex] yards, these measurements are not equivalent.
[tex]$\textbf{Option C: }$[/tex]
Here we compare [tex]$320$[/tex] seconds to [tex]$5$[/tex] minutes [tex]$20$[/tex] seconds.
Since
[tex]$$1 \text{ minute} = 60 \text{ seconds},$$[/tex]
[tex]$5$[/tex] minutes is
[tex]$$5 \times 60 = 300 \text{ seconds}.$$[/tex]
Adding the extra [tex]$20$[/tex] seconds gives
[tex]$$300 + 20 = 320 \text{ seconds}.$$[/tex]
This means that [tex]$320$[/tex] seconds is exactly [tex]$5$[/tex] minutes and [tex]$20$[/tex] seconds.
[tex]$\textbf{Option D: }$[/tex]
We check if [tex]$2.5$[/tex] miles equals [tex]$13,\!200$[/tex] feet.
Since
[tex]$$1 \text{ mile} = 5280 \text{ feet},$$[/tex]
then
[tex]$$2.5 \text{ miles} = 2.5 \times 5280\,\text{ft} = 13,\!200\,\text{ft}.$$[/tex]
The measurements match exactly.
[tex]$\textbf{Option E: }$[/tex]
We need to determine if [tex]$60$[/tex] inches equals [tex]$4$[/tex] feet.
Remember that
[tex]$$1 \text{ foot} = 12 \text{ inches},$$[/tex]
so
[tex]$$60 \text{ inches} = \frac{60}{12} \text{ feet} = 5 \text{ feet},$$[/tex]
which is not equal to [tex]$4$[/tex] feet.
[tex]$\textbf{Final Answer:}$[/tex]
The equivalent measurements are in Options A, C, and D.
[tex]$\textbf{Option A: }$[/tex]
We compare [tex]$15$[/tex] kilometers with [tex]$1,\!500,\!000$[/tex] centimeters.
Since
[tex]$$1 \text{ km} = 100,\!000 \text{ cm},$$[/tex]
then
[tex]$$15 \text{ km} = 15 \times 100,\!000\,\text{cm} = 1,\!500,\!000\,\text{cm}.$$[/tex]
This shows the two measurements are equal.
[tex]$\textbf{Option B: }$[/tex]
We need to see if [tex]$28$[/tex] feet is equal to [tex]$9$[/tex] yards.
Recall that
[tex]$$1 \text{ yard} = 3 \text{ feet},$$[/tex]
so
[tex]$$28 \text{ ft} = \frac{28}{3} \text{ yards} \approx 9.\overline{3}\text{ yards}.$$[/tex]
Since [tex]$9.\overline{3}$[/tex] yards is not equal to [tex]$9$[/tex] yards, these measurements are not equivalent.
[tex]$\textbf{Option C: }$[/tex]
Here we compare [tex]$320$[/tex] seconds to [tex]$5$[/tex] minutes [tex]$20$[/tex] seconds.
Since
[tex]$$1 \text{ minute} = 60 \text{ seconds},$$[/tex]
[tex]$5$[/tex] minutes is
[tex]$$5 \times 60 = 300 \text{ seconds}.$$[/tex]
Adding the extra [tex]$20$[/tex] seconds gives
[tex]$$300 + 20 = 320 \text{ seconds}.$$[/tex]
This means that [tex]$320$[/tex] seconds is exactly [tex]$5$[/tex] minutes and [tex]$20$[/tex] seconds.
[tex]$\textbf{Option D: }$[/tex]
We check if [tex]$2.5$[/tex] miles equals [tex]$13,\!200$[/tex] feet.
Since
[tex]$$1 \text{ mile} = 5280 \text{ feet},$$[/tex]
then
[tex]$$2.5 \text{ miles} = 2.5 \times 5280\,\text{ft} = 13,\!200\,\text{ft}.$$[/tex]
The measurements match exactly.
[tex]$\textbf{Option E: }$[/tex]
We need to determine if [tex]$60$[/tex] inches equals [tex]$4$[/tex] feet.
Remember that
[tex]$$1 \text{ foot} = 12 \text{ inches},$$[/tex]
so
[tex]$$60 \text{ inches} = \frac{60}{12} \text{ feet} = 5 \text{ feet},$$[/tex]
which is not equal to [tex]$4$[/tex] feet.
[tex]$\textbf{Final Answer:}$[/tex]
The equivalent measurements are in Options A, C, and D.
