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Geometry and Measurement Videos 88 videos

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Calculating the Bisector Length of a Square 2 Views


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Description:

The figure above is a square with a side length of . What is the length of ?


Transcript

00:02

Okay Satay shmoop er's Another picture for you We got

00:05

a b c d here and one side's five times

00:08

grow to this looks like a square but we don't

00:10

see any of those right angle thing You so we

00:12

can assume it yet let's See what they say the

00:15

figure above the square Ok so what now We can

00:17

assume it with a side of length Five times where

00:20

to what's the length of a d All right Well

00:26

see the problem is special here You sure all problems

00:29

are unique Yes Your all problems are unique snowflakes whose

00:33

parents love them very much But cutting this square in

00:36

half makes two special right triangles So this problem is

00:39

well you know extra special So we just put in

00:41

the forty five degree lines there in a little box

00:44

thing He's there you had partial credit You'd lose Get

00:47

two points for all that Well the ninety degree corners

00:49

are perfectly divided in half by that by sector So

00:52

that splits the angle into two forty five degree angles

00:54

When the angles of a right triangle are forty five

00:56

forty five and ninety the triangle is called Yes a

00:59

special triangle So there we go We've got x and

01:02

then x and x times grow too well The two

01:05

legs are equal courtesy of the two equal angles and

01:08

the high pot news is a screw to two times

01:10

greater than legs Well one of the sides already has

01:13

a square to to there But if we multiply that

01:15

by the square root of to to get a d

01:17

well what happens This happens It looks like this five

01:20

times grow two times Two is five times two or

01:23

just ten So eighty is ten that's it And yes

01:27

we could've used the pythagorean theorem in the beginning and

01:29

just squared all sides and gotten you know square root

01:32

of this five times for two squared plus five from

01:34

room c squared You'll get fifty plus fifty a c

01:37

squared or one hundred and it's road one hundred ten

01:40

Yeah The diagram of the square can't equal the length

01:42

of the side so that sea would have been impossible

01:46

in the length of five times were over too well

01:48

that comes from cutting one of the sides in half

01:50

If you remember the this ratio this acts money maximum

01:54

Ratio for a forty five Forty five Ninety triangle but

01:56

to divide length by expert to instead of multiply well

01:59

then we'd get a diagonal of five as in be

02:02

so that ain't it either So just go with the 00:02:05.21 --> [endTime] war shmoop

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