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FInd the perimeter of the image

Mathematics
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37 units 38 units 39 units 40 units
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to find the perimeter of given shape, you need to find out sides first

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Other answers:

perimeter = sum of all sides
know how to find the length of sides on coordinate plane ?
distance formula ?
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
there is a simpler way to do this, which uses the distance formula in disguise...
ok..
whats the simpler way ?
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use pythagorean theorem : that red side = \(\sqrt{2^2+6^2} = \sqrt{40}\)
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...
use whichever u feel is easy...
how did u solve that ^ ... like how did u get 40 ?
the goal is to find the length of all sides and add up
ok..
did u get how I got : red side = \(\sqrt{2^2+6^2} \)
?
i know how u got the 2 and the 6... just not the 40 ...
oh cool :) ive just skipped a step : red side = \(\sqrt{2^2+6^2} = \sqrt{4+36} = ?\)
ohhh ok
find the lengths of remaining sides in any way u wish, and add them all up
for pt it would be 4^2 + 10^2
which is 116
Yes ! dont forget the sqrt
ok...
\(PT^2 = 4^2 + 10^2\) \(PT = \sqrt{4^2 + 10^2} = \sqrt{116}\)
TS is 7
how do i do SR O.o
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50 ok..
*sqrt...
right... lol and then the last side is sqrt 61 ?
do i add them all ?
yup ! perimeter = length around a shape = sum of all sides
sqrt 274
?
lol no
you cannot add radicals like that
\(\large \sqrt{a} + \sqrt{b} + \sqrt{c} ~ \ne ~ \sqrt{a + b+ c}\)
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
hm i got 60 ;/
You got : \(QP = \sqrt{40}\) \(PT = \sqrt{116}\) \(TS = 7\) \(SR = \sqrt{50}\) \(RQ = \sqrt{61}\)
right ?
yes
plug each sqrt in ur calcualtor and add them all
\(QP = \sqrt{40} = \color{red}{6.32}\) \(PT = \sqrt{116} = \color{red}{10.77}\) \(TS = 7 = \color{red}{7}\) \(SR = \sqrt{50} = \color{red}{7.07}\) \(RQ = \sqrt{61} = \color{red}{7.81}\) --------------------------------------- perimeter = \(\color{Red}{?}\)
38. 97
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
so should i put 39 ?
or try it the long way to double check
rounding it becomes : \(38.97 \approx 39\)
Nope, both are one and same... you may try for practice if u want maybe :)
okay :) thank you!
np :)

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