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SAT Math 9.4 Geometry and Measurement 184 Views


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SAT Math 9.4 Geometry and Measurement

Language:
English Language

Transcript

00:03

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

00:06

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

00:10

The cue ball keeps getting in the way.

00:12

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

00:17

The fourth side is adjacent to a long wall.

00:21

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

00:28

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.

00:36

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

00:39

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

00:43

We know it’s 10 feet wide…

00:45

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

00:48

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

00:52

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.

01:04

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

01:08

Doesn’t matter how big the pool is.

01:09

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

01:16

Altogether then, we have 30x plus 200.

01:20

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

01:25

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

01:29

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

01:34

Option B is 18…but don’t fall for it!

01:37

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

01:43

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

01:49

Choice D and we're done.

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