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Mathematics 51 Online
OpenStudy (anonymous):

A running track in the shape of an oval is shown. The ends of the track form semicircles. A running track is shown. The left and right edges of the track are identical curves. The top and bottom edges of the track are straight lines. The track has width 68 m and length of one straight edge 140 m. What is the perimeter of the inside of the track? (π = 3.14) 416.00 m 493.52 m 707.04 m 719.60 m

OpenStudy (anonymous):

@Loser66

OpenStudy (michele_laino):

the perimeter of the running track, is given by the sum of the length of each side, so we have this formula: \[p = \left( {\pi \cdot 34} \right) + 140 + \left( {\pi \cdot 34} \right) + 140 = ...?\]

OpenStudy (anonymous):

493.22? @Michele_Laino

OpenStudy (anonymous):

493.52*

OpenStudy (michele_laino):

correct! It is \(493.52\) meters

OpenStudy (anonymous):

Thanks so much! Do you mind helping on another question?

OpenStudy (michele_laino):

ok!

OpenStudy (anonymous):

Which of the following possibilities will form a triangle? Side = 15 cm, side = 7 cm, side = 7 cm Side = 15 cm, side = 7 cm, side = 9 cm Side = 14 cm, side = 6 cm, side = 7 cm Side = 14 cm, side = 6 cm, side = 8 cm

OpenStudy (michele_laino):

hint: for a triangle, each side has to be greather than the difference between the other two sides

OpenStudy (michele_laino):

greater*

OpenStudy (michele_laino):

furthermore, each side has to be less than the sum of other two sides

OpenStudy (michele_laino):

please, I consider the first case: we have the subsequent difference: 15-7= 8 which is greater than 7, so what can you conclude

OpenStudy (anonymous):

im trying to write everything on paper just incase I have to use this for later. give me a second.

OpenStudy (michele_laino):

ok!

OpenStudy (anonymous):

The sum is equal to one of the sides, so that cant be.. right?

OpenStudy (michele_laino):

we have: third side = 7 < 15 - 7=8, so it can be a triangle

OpenStudy (michele_laino):

third case, we have this: 14 < 6+7 = 13, so what can you conclude?

OpenStudy (michele_laino):

oops, 14 > 6+7= 13...

OpenStudy (anonymous):

Sorry, im trying to work it out (:

OpenStudy (michele_laino):

no problem :)

OpenStudy (anonymous):

I know C cant be right... right?

OpenStudy (anonymous):

But it seems like A and B could be right..

OpenStudy (michele_laino):

the side = 14 is greater than the sum of the other two sides, which is 13, so it can not be a triangle

OpenStudy (michele_laino):

case D. is wrong since the difference between two sides 14-8= 6 which is not less than the third side. So, the right option is B.

OpenStudy (anonymous):

Oh okay.. I understand now... Thank you! I still have 2 more questions.. do you mind helping me or should I close this post?

OpenStudy (michele_laino):

yes! please open a new post

OpenStudy (anonymous):

ok, should I tag you in the new post?

OpenStudy (michele_laino):

ok!

OpenStudy (anonymous):

okay, thanks so much!

OpenStudy (michele_laino):

:)

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