Certainly! Let's analyze the given proportion and options step-by-step.
The proportion we need to consider is:
[tex]\[
\frac{15 \text{ cm}}{5 \text{ cm}} = 3
\][/tex]
This means that for every 5 cm, we have 15 cm. The multiplicative factor here is [tex]\(3\)[/tex].
Now let's check each of the options to see which ones correctly match this proportion. Each option follows the format:
[tex]\[
\text{cm value} \times \text{multiplier} \stackrel{}{=} \text{result}
\][/tex]
We need to verify if:
[tex]\[
\text{cm value} \times 3 = \text{result}
\][/tex]
Let's analyze each option in the table one by one:
1. First Option:
[tex]\[
5 \text{ cm} \times 3 = 15 \text{ cm}
\][/tex]
This matches because [tex]\(5 \times 3 = 15\)[/tex].
2. Second Option:
[tex]\[
9 \text{ cm} \times 3 = 27 \text{ cm}
\][/tex]
This matches because [tex]\(9 \times 3 = 27\)[/tex].
3. Third Option:
[tex]\[
2 \text{ cm} \times 3 = 6 \text{ cm}
\][/tex]
This matches because [tex]\(2 \times 3 = 6\)[/tex].
4. Fourth Option:
[tex]\[
11 \text{ cm} \times 3 = 33 \text{ cm}
\][/tex]
This matches because [tex]\(11 \times 3 = 33\)[/tex].
So, all the given options correctly match the proportion, as they all validate the equation [tex]\( \text{cm value} \times 3 = \text{result} \)[/tex].
In conclusion, the following options correctly match the given proportion of [tex]\(\frac{15 \text{ cm}}{5 \text{ cm}} = 3\)[/tex]:
[tex]\[
(5 \text{ cm}, 3, 15 \text{ cm})
\][/tex]
[tex]\[
(9 \text{ cm}, 3, 27 \text{ cm})
\][/tex]
[tex]\[
(2 \text{ cm}, 3, 6 \text{ cm})
\][/tex]
[tex]\[
(11 \text{ cm}, 3, 33 \text{ cm})
\][/tex]
