Question

Pappy's Pond is located close to an elementary school. The city plans to fence it in to keep small children from accessing the water. What is the perimeter of a triangular-shaped fence the city can place around the pond, using integer coordinates (no decimals) on the grid? You must show all work to receive credit.

Answer 1

you gotta enclose the whole thing right?

Answer 2

yes

Answer 3

oh i thought it was a rectangle, but it has to be a triangle
damn

Answer 4

darn

Answer 5

looks like \((0,0)\) to \((2,8)\) to \((10,0)\) would do it doesn't it?

Answer 6

yea

Answer 7

k then we can do that one i think
find the perimeter i mean

Answer 8

idk how

Answer 9

from \((0,0)\) to \((10,0)\) you just count and get \(10\)

Answer 10

the other two require the distance formula
do you know it ?

Answer 11

no

Answer 12

it is pythagoras basically
from \((0,0)\) to \((2,8)\) you have a triangle with one side \(2\) and the other side \(8\) so the distance (hypotenuse) is
\[\sqrt{2^2+8^2}=\sqrt{4+64}=\sqrt{68}\]

Answer 13

not sure how you can do this problem without the distance formula or some such thing
does that ring a bell at all?

Answer 14

then from \((2,8)\) to \((10,0)\) the distance is
\[\sqrt{8^2+8^2}=\sqrt{64+64}=\sqrt{128}\] or if you prefer
\[8\sqrt2\]

Answer 15

is that the answer

Answer 16

does this look at all familiar to you?

Answer 17

to get an answer you would have to add them up
\[10+\sqrt{68}+\sqrt{128}\]

Answer 18

i think you would get a different answer if you used different points
so there would be no one right answer

Answer 19

8.246+10+11.313?

Answer 20

29.559?

Answer 21

i guess if you used a calculator

Answer 22

but thats the answer

Answer 23

ok

Answer 24

?

Answer 25

http://www.wolframalpha.com/input/?i=sqrt%2868%29%2Bsqrt%28128%29%2B10

Answer 26

looks good to me

Answer 27

thanks could you help w another