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SAT Math 4.1 Geometry and Measurement 193 Views


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Description:

SAT Math 4.1 Geometry and Measurement

Language:
English Language

Transcript

00:02

Here’s your shmoop du jour, brought to you by diagonal lines.

00:06

Without them, every other necktie would have a fish on it.

00:11

What is the length of the diagonals of a rectangle with sides equal to x and 2x?

00:17

Here are the potential answers...

00:21

Hm…when might we see a rectangle with diagonals in real life…?

00:26

Perhaps we’re looking at a Confederate flag...

00:29

…or that quilt your grandmother stitched for you…

00:31

…or a dead Sasquatch floating in our swimming pool…

00:34

Yeah, let’s go with the Sasquatch. We can’t bear to look at that quilt again.

00:38

Okay, so if your pool has a width of x and a length of 2x…

00:42

…we want to know the length of the Sasquatch,

00:44

from the end of one hand to the tip of his opposite enormous foot.

00:50

What we should immediately recognize is that the diagonal of any rectangle divides the

00:55

shape into two equally sized triangles.

00:58

So as long as we know how to determine the hypotenuse of

01:01

a right triangle given the length of its legs…this should be a cinch.

01:04

We’re going to fall back on our a squared plus b squared equals c squared formula…

01:09

…so x squared plus 2x squared equals c squared. So let's rewrite it...

01:14

2x squared is 4x squared… added to our one x squared.

01:19

That gives us 5x squared equals c squared.

01:22

We can take the square root of both sides to get x√5 = c.

01:27

So our answer is C.

01:29

Such a bummer that we’re going to have to put up with that stench another three days.

01:32

The pool guy doesn’t come until Tuesday…

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