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anonymous
 one year ago
A triangle has vertices at (2, 4), (3, 6), and (4, 2). Find its perimeter rounded to two decimal places.
anonymous
 one year ago
A triangle has vertices at (2, 4), (3, 6), and (4, 2). Find its perimeter rounded to two decimal places.

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freckles
 one year ago
Best ResponseYou've already chosen the best response.0I would plot the points so it is easier for me to see which three distances to calculate.

freckles
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437665201466:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437665261302:dw we need to find all three side measurements to do that we can use the distance formula so for example let's go ahead and find the distance between (2,4) and (4,2) you do that by doing: \[d_1=\sqrt{(24)^2+(4(2))^2} \\ d_1=\sqrt{(2)^2+(6)^2} \\ d_1=\sqrt{4+36} \\ d_1=\sqrt{40}\] so we have thatdw:1437665356288:dw we also need to find the other side lengths you try the other two legs and remember: \[\text{ The distance \between } (x_1,y_1) \text{ and } (x_2,y_2) \text{ is } \\ \sqrt{(x_1x_2)^2+(y_1y_2)^2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0once you find all the side lengths you add the side lengths to find the perimeter

freckles
 one year ago
Best ResponseYou've already chosen the best response.0so have you computed the distance between (2,4) and (3,6) ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437665675706:dw well you still need to find these two distances (these two side lengths)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0that is you need to find the distance between (2,4) and (3,6) you also need to find the distance between (3,6) and (4,2)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0the distance between (2,4) and (3,6) is given by: \[d_3=\sqrt{(2(3))^2+(4(6))^2}=\sqrt{5^2+(10)^2}\] see if you can finish simplifying this

freckles
 one year ago
Best ResponseYou've already chosen the best response.0do you mean sqrt(125) for d_3 ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437665932861:dw now you just need to find d_2

freckles
 one year ago
Best ResponseYou've already chosen the best response.0which is the distance between (4,2) and (3,6)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0use that formula above to find it

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[\text{ The distance between } (x_1,y_1) \text{ and } (x_2,y_2) \text{ is } \\ \sqrt{(x_1x_2)^2+(y_1y_2)^2} \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0hmm... that is what you got for the other one... try again... you have (4,2) and (3,6) replace x1 with 4 replace x2 with 3 replace y1 with 2 replace y2 with 6 ... \[d_2=\sqrt{(4(3))^2+(2(6))^2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.04(3) is the same as 4+3 2(6) is the same as 2+6

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[d_2=\sqrt{(4+3)^2+(2+6)^2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0compute 4+3 and 2+6 then square both results

freckles
 one year ago
Best ResponseYou've already chosen the best response.0then add those results

freckles
 one year ago
Best ResponseYou've already chosen the best response.0sounds like you are doing (4+3)+(2+6) which means you are ignoring the squares

freckles
 one year ago
Best ResponseYou've already chosen the best response.0(4+3)^2=(7)^2 (2+6)^2=(4)^2

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[d_2=\sqrt{(4+3)^2+(2+6)^2} \\ d_2=\sqrt{(7)^2+(4)^2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0you square the numbers before adding them because that is what order of operations tells us to do

freckles
 one year ago
Best ResponseYou've already chosen the best response.0don't know where the 29 comes from but sqrt(49+16) is sqrt(65)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437666447857:dw now add all the sides to find the perimeter

freckles
 one year ago
Best ResponseYou've already chosen the best response.0so you added sqrt(125) and sqrt(40) and sqrt(65)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0or did you add 125 and 40 and 65?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0because those aren't the same numbers

freckles
 one year ago
Best ResponseYou've already chosen the best response.0sqrt(125) is not the same as 125 sqrt(40) is not the same as 40 sqrt(65) is not the same as 65 so adding sqrt(125) and sqrt(40) and sqrt(65) is not equivalent to adding 125 and 40 and 65.

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt{125}+\sqrt{40}+\sqrt{65}\] just enter this into the calculator to get the approximated perimeter

freckles
 one year ago
Best ResponseYou've already chosen the best response.0ok and you are suppose to round to 2 decimal places so that would actually be...
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