På den lekplatsen finns både en gunga och en lång rutschkana.

Because Swedish often puts the location first when that is the topic the speaker wants to highlight.

Here, På den lekplatsen means on/at that playground, and it sets the scene first. After that, Swedish main clauses follow the V2 rule: the finite verb must come in the second position. So the verb finns comes right after the opening phrase.

Compare:

• På den lekplatsen finns både en gunga och en lång rutschkana.
• Det finns både en gunga och en lång rutschkana på den lekplatsen.

Both are possible, but the first one emphasizes the playground more.

Because på is the normal preposition for being at/on a playground in Swedish.

English speakers often expect i because English uses in for many places, but Swedish uses different location patterns. A playground is thought of more as an open area or surface, so på lekplatsen is idiomatic.

So:

• på lekplatsen = at/on the playground
• i would usually suggest being inside something more enclosed

Finns is the present tense of finnas, and in sentences like this it means there is or there are.

So:

• det finns en gunga = there is a swing
• det finns två gungor = there are two swings

It is used to talk about existence or presence, not identity.

Because Swedish uses finns for saying that something exists or is present somewhere.

Use är for identity, description, or state:

• Det är en gunga. = It is a swing.
• Gungan är långsam. = The swing is slow.

But if you want to say a swing is located somewhere, you normally use finns:

• På lekplatsen finns en gunga. = There is a swing on the playground.

So finns is the natural choice here.

In basic existential sentences, Swedish often uses det finns:

• Det finns en gunga på lekplatsen.

But when another element is moved to the front, especially a place phrase like På den lekplatsen, the dummy subject det is usually left out:

• På den lekplatsen finns en gunga.

So the sentence is not missing anything. This is normal Swedish word order.

It means both ... and ...

In this sentence:

• både en gunga och en lång rutschkana
  = both a swing and a long slide

This structure joins two things and emphasizes that both are present, not just one of them.

Other examples:

• Hon talar både svenska och engelska. = She speaks both Swedish and English.
• Jag gillar både kaffe och te. = I like both coffee and tea.

Because the sentence is introducing these things as items that are present there, not referring to specific already-known ones.

In existential sentences with finns, Swedish often uses indefinite nouns:

• Det finns en gunga där. = There is a swing there.

If you used the definite form, it would sound like you mean a specific swing or slide already known from context:

• gungan = the swing
• rutschkanan = the slide

So the indefinite forms are the natural choice here.

Yes. Both gunga and rutschkana are common-gender nouns, so they take en in the singular.

That is why you get:

• en gunga
• en rutschkana

And also:

• den lekplatsen

because lekplats is also an en-word.

Because rutschkana is:

• singular
• indefinite
• common gender

For an adjective with a singular indefinite en-word, Swedish normally uses the basic form:

• en lång rutschkana

Compare:

• en lång rutschkana = common gender singular indefinite
• ett långt rep = neuter singular indefinite
• långa rutschkanor = plural
• den långa rutschkanan = definite

So lång is exactly the form you expect here.

Den lekplatsen means something like that playground or the playground in question, depending on context.

The word den here points to a specific playground. It makes the reference more definite and more specific than just lekplatsen.

Compare:

• lekplatsen = the playground
• den lekplatsen = that playground / that particular playground

A learner may also notice that Swedish often uses den/det/de with nouns to point something out, especially in speech and everyday language.

Yes. Rutschkana is a compound noun, and compound nouns are very common in Swedish.

• rutschkana = slide
• lekplats = playground

In Swedish compounds, the last part is the main noun, and it determines the grammatical gender and inflection. So in rutschkana, the final part is kana, which is why the whole word behaves like an en-word:

• en rutschkana
• rutschkanan
• rutschkanor

Learning to spot compounds is very useful in Swedish.

Yes. A very natural alternative is:

• Det finns både en gunga och en lång rutschkana på den lekplatsen.

This version starts with det finns, which is the most basic way to say there is/there are.

The original sentence:

• På den lekplatsen finns både en gunga och en lång rutschkana

is also natural, but it puts more focus on the location first.

So the difference is mainly about emphasis and information order, not basic meaning.

Och still means and, but together with både, it forms the fixed pair både ... och ... = both ... and ...

So in this sentence, och is not just adding one thing to another in a neutral way. It is part of a structure that emphasizes that both items are included.

Compare:

• en gunga och en rutschkana = a swing and a slide
• både en gunga och en rutschkana = both a swing and a slide

The second version sounds a bit more emphatic.