Question

FInd the perimeter of the image

Answer 1

37 units

38 units

39 units

40 units

Answer 2

@ash2326 @phi

Answer 3

to find the perimeter of given shape, you need to find out sides first

Answer 4

perimeter = sum of all sides

Answer 5

know how to find the length of sides on coordinate plane ?

Answer 6

distance formula ?

Answer 7

yes, but for that u need to figure out coordinates of points and plug them in the formula... which is a pain... and u need to do it for 5 times... since u have 5 sides

Answer 8

there is a simpler way to do this, which uses the distance formula in disguise...

Answer 9

ok..

Answer 10

whats the simpler way ?

Answer 11

use pythagorean theorem :

that red side = \(\sqrt{2^2+6^2} = \sqrt{40}\)

Answer 12

this is exact same as distance formula,
but this is felt simple because, you're not plugging in the coordinates...
instead you're just counting the number of grids...

Answer 13

use whichever u feel is easy...

Answer 14

how did u solve that ^ ... like how did u get 40 ?

Answer 15

the goal is to find the length of all sides and add up

Answer 16

ok..

Answer 17

did u get how I got :

red side = \(\sqrt{2^2+6^2} \)

Answer 18

?

Answer 19

i know how u got the 2 and the 6... just not the 40 ...

Answer 20

oh cool :) ive just skipped a step :

red side = \(\sqrt{2^2+6^2} = \sqrt{4+36} = ?\)

Answer 21

ohhh ok

Answer 22

find the lengths of remaining sides in any way u wish,
and add them all up

Answer 23

for pt it would be 4^2 + 10^2

Answer 24

which is 116

Answer 25

Yes ! dont forget the sqrt

Answer 26

ok...

Answer 27

\(PT^2 = 4^2 + 10^2\)

\(PT = \sqrt{4^2 + 10^2} = \sqrt{116}\)

Answer 28

TS is 7

Answer 29

how do i do SR O.o

Answer 30

50 ok..

Answer 31

*sqrt...

Answer 32

right... lol and then the last side is sqrt 61 ?

Answer 33

do i add them all ?

Answer 34

yup !

perimeter = length around a shape
= sum of all sides

Answer 35

sqrt 274

Answer 36

?

Answer 37

lol no

Answer 38

you cannot add radicals like that

Answer 39

\(\large \sqrt{a} + \sqrt{b} + \sqrt{c} ~ \ne ~ \sqrt{a + b+ c}\)

Answer 40

http://www.wolframalpha.com/input/?i=sqrt%282%5E2%2B6%5E2%29+%2B+sqrt%284%5E2%2B10%5E2%29+%2B+7+%2B+sqrt%281%5E2%2B7%5E2%29+%2B+sqrt%286%5E2+%2B+5%5E2%29

Answer 41

hm i got 60 ;/

Answer 42

You got :

\(QP = \sqrt{40}\)
\(PT = \sqrt{116}\)
\(TS = 7\)
\(SR = \sqrt{50}\)
\(RQ = \sqrt{61}\)

Answer 43

right ?

Answer 44

yes

Answer 45

plug each sqrt in ur calcualtor and add them all

Answer 46

\(QP = \sqrt{40} = \color{red}{6.32}\)
\(PT = \sqrt{116} = \color{red}{10.77}\)
\(TS = 7 = \color{red}{7}\)
\(SR = \sqrt{50} = \color{red}{7.07}\)
\(RQ = \sqrt{61} = \color{red}{7.81}\)
---------------------------------------
perimeter = \(\color{Red}{?}\)

Answer 47

38. 97

Answer 48

wolfram says the same :
http://www.wolframalpha.com/input/?i=sqrt%2840%29+%2B+sqrt%28116%29+%2B+7+%2B+sqrt%2850%29+%2B+sqrt%2861%29

Answer 49

so should i put 39 ?

Answer 50

or try it the long way to double check

Answer 51

rounding it becomes :

\(38.97 \approx 39\)

Answer 52

Nope, both are one and same...
you may try for practice if u want maybe :)

Answer 53

okay :) thank you!

Answer 54

np :)