To find the height of the building and determine which ratio corresponds to the height of the building to its shadow, we can follow these steps:
1. Identify the known values:
- Height of the pole: [tex]\(6\)[/tex] meters
- Length of the pole's shadow: [tex]\(10\)[/tex] meters
- Length of the building's shadow: [tex]\(220\)[/tex] meters
2. Determine the ratio of the height of the pole to the length of its shadow:
- The ratio of the pole's height to its shadow is [tex]\(\frac{6}{10}\)[/tex].
3. Use the ratio to find the height of the building:
- Let the height of the building be [tex]\(h\)[/tex] meters.
- The ratio is the same for both the pole and the building, so we have:
[tex]\[
\frac{h}{220} = \frac{6}{10}
\][/tex]
- Solving for [tex]\(h\)[/tex]:
[tex]\[
h = \left(\frac{6}{10}\right) \times 220
\][/tex]
- Calculate [tex]\(h\)[/tex]:
[tex]\[
h = \frac{6 \times 220}{10} = \frac{1320}{10} = 132
\][/tex]
- So, the height of the building is [tex]\(132\)[/tex] meters.
4. Determine which ratio corresponds to the height of the building to its shadow:
- We know the ratio of the building's height to its shadow can be reduced to:
[tex]\[
\frac{132}{220}
\][/tex]
- Simplify this ratio:
[tex]\[
\frac{132}{220} = \frac{6}{10} = \frac{3}{5}
\][/tex]
By comparing the provided ratio choices:
- [tex]\(\frac{3}{5}\)[/tex]
- [tex]\(\frac{5}{3}\)[/tex]
- [tex]\(3\)[/tex]
The correct ratio that corresponds to the height of the building to its shadow is [tex]\(\frac{3}{5}\)[/tex], which is the first choice.
Therefore, the height of the building is [tex]\(132\)[/tex] meters, and the correct ratio is [tex]\(\frac{3}{5}\)[/tex].
