Math Is Fun Forum

apsara123

Member

Registered: 2016-05-14

Posts: 20

HELP with 3 questions

1.Kendra has an unlimited supply of unbreakable sticks of length 2, 4 and 6 inches. Using these sticks, how many non-congruent triangles can she make if each side is made with a whole stick? Two sticks can be joined only at a vertex of the triangle. (A triangle with sides of length 4, 6, 6 is an example of one such triangle to be included, whereas a triangle with sides of length 2, 2, 4 should not be included.)

2.Points $D$, $E$, and $F$ are the midpoints of sides $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$ of $\triangle ABC$, respectively, and $\overline{CZ}$ is an altitude of the triangle. If $\angle BAC = 71^\circ$, $\angle ABC = 39^\circ$, and $\angle BCA = 70^\circ$, then what is $\angle EZD+\angle EFD$ in degrees?

3.In triangle $ABC$, the medians $\overline{AD}$, $\overline{BE}$, and $\overline{CF}$ concur at the centroid $G$.

(a) Prove that $AD < (AB + AC)/2$.

(b) Let $P=AB+AC+BC$ be the perimeter of $\triangle ABC.$ Prove that
\[\frac{3P}{4} < AD + BE + CF < P.\]

I need help with these 3 problems, thank you!!!

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: HELP with 3 questions

I have given hint for Q3. in the thread below
http://www.mathisfunforum.com/viewtopic.php?id=23062

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: HELP with 3 questions

hi apsara123

I would do Q1 just by listing all the possible combinations of 2,4 and 6 and eliminating those that don't make a triangle. 

Q2.  See http://www.mathisfunforum.com/viewtopic.php?id=22423

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: HELP with 3 questions

Last edited by thickhead (2016-05-18 20:16:56)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Re: HELP with 3 questions

i still cant seem to get Q3 part b.
I created tons of inequalities and put them in terms of other lines.
Then I added some of the inequalities together and I couldn't get the rest

apsara123

Member

Registered: 2016-05-14

Posts: 20

Re: HELP with 3 questions

I need help with
Randy presses RAND on his calculator twice to obtain two random numbers between 0 and 1. Let $p$ be the probability that these two numbers and 1 form the sides of an obtuse triangle. Find $4p$.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: HELP with 3 questions

i still cant seem to get Q3 part b.
I created tons of inequalities and put them in terms of other lines.
Then I added some of the inequalities together and I couldn't get the rest

Last edited by thickhead (2016-05-19 16:12:39)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: HELP with 3 questions

I need help with
Randy presses RAND on his calculator twice to obtain two random numbers between 0 and 1. Let $p$ be the probability that these two numbers and 1 form the sides of an obtuse triangle. Find $4p$.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: HELP with 3 questions

Hi;

I need help with
Randy presses RAND on his calculator twice to obtain two random numbers between 0 and 1. Let $p$ be the probability that these two numbers and 1 form the sides of an obtuse triangle. Find $4p$.

This is a fairly well known problem:

http://math.stackexchange.com/questions … es/1781615

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: HELP with 3 questions

# apsara123 had put up today again problems 2 & 3 in a new thread. I was answering it. Something happened and it is not to be seen now. How? Can anybody explain?

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: HELP with 3 questions

Hi;

It was because that post was a duplicate of this one right here. Your post underneath his was just a link to this one. Keeping all relevant work together is one of my responsibilities. During this time of year there will be some duplicates of questions. In the interest of clarity I try to keep similar questions along with their answers together. Sorry for the inconvenience.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: HELP with 3 questions

O.K. thank you. The mystery is cleared.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}