ShmoopTube

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Here’s your shmoop du jour, brought to you by swimming pools.

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We’ve tried to swim a few laps, but we can’t quite get the hang of it.

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The cue ball keeps getting in the way.

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A deck 10 feet wide is built around three sides of a square pool.

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The fourth side is adjacent to a long wall.

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If the area of the deck is 740 ft2, what is the area of the pool?

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Here are the potential answers...

00:32

Rather than just look at words on a page, it helps to visualize, so let’s… do so.

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Here’s our pool. We have no idea yet how big it is.

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And…here’s our deck. It surrounds the pool on three sides.

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We know it’s 10 feet wide…

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…so, let’s break this deck down a bit, into more manageable pieces.

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Now we’ve got 5 distinct sections… and we're gonna label them…

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The sections touching the pool are going to have an area of 10x, with x being the unknown length.

00:59

We’ve got three of those, so…3 times 10x, or 30x.

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Now for the corner sections, those are DEFINITELY going to be 10 x 10.

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Doesn’t matter how big the pool is.

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We have 2 of those, or… 2 times 10 times 10. Which is 200 square feet.

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Altogether then, we have 30x plus 200.

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We can set that equal to the 740 square feet we’re given…

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…subtract 200 from both sides to get 30x = 540…

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…then divide both sides by 30 to get x = 18.

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Option B is 18…but don’t fall for it!

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We’ve got the measure of one side of the square pool… but we need to square it to get the pool’s area.

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18 squared is 324… so the pool is 324 square feet.

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Choice D and we're done.

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