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There are two trampoline runways at a gymnastics practice facility. Both runways are [tex]\sqrt{3}[/tex] meters wide. One is [tex]6\sqrt{3}[/tex] meters long, and the other is [tex]5\sqrt{2}[/tex] meters long.

What is the total area of the trampoline runways?

Answer :

To find the total area of the trampoline runways, we'll calculate the area for each runway separately and then add them together.

1. Understand the Dimensions:
- Both runways are [tex]\(\sqrt{3}\)[/tex] meters wide.
- The first runway is [tex]\(6 \sqrt{3}\)[/tex] meters long.
- The second runway is [tex]\(5 \sqrt{2}\)[/tex] meters long.

2. Calculate the Area of the First Runway:
- Area is found by multiplying width and length.
- For the first runway:
[tex]\[
\text{Area}_1 = \sqrt{3} \times 6\sqrt{3}
\][/tex]
- Simplify:
[tex]\[
= \sqrt{3} \times 6 \times \sqrt{3} = 6 \times 3 = 18 \text{ square meters}
\][/tex]

3. Calculate the Area of the Second Runway:
- Using the same method:
[tex]\[
\text{Area}_2 = \sqrt{3} \times 5\sqrt{2}
\][/tex]
- Simplify:
[tex]\[
= \sqrt{3} \times 5 \times \sqrt{2} = 5 \times \sqrt{6} \approx 12.247 \text{ square meters}
\][/tex]

4. Calculate the Total Area:
- Add the two areas together:
[tex]\[
\text{Total Area} = 18 + 12.247 = 30.247 \text{ square meters}
\][/tex]

Thus, the total area of the two trampoline runways is approximately 30.247 square meters.

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