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 Post subject: isosceles trianglePosted: Sat Jan 09, 2016 10:47 am

Joined: Sat Jan 09, 2016 10:32 am
Posts: 5
can anyone help to solve this problem?
In an isosceles triangle, twice one of the angles is 5 times as big as another. What is not a possible size for one of the angles?
The options are 100, 75,40,30,20

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 11:37 am

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 7140
Location: East Kent
In an isosceles triangle 2 of the angles are the same.
You can use this fact and trial and error.

Also you cannot exceed the maximum number of degrees in a triangle.

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 12:04 pm

Joined: Tue Oct 27, 2009 8:19 pm
Posts: 6822
Here the answer is 20 apparently

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 1:24 pm

Joined: Sun Oct 19, 2014 11:52 am
Posts: 60
and using algebra...

If,

x = the size of one of the equal pair of angles.
y = the third angle.

We have two sets of equations (possibilities):

2x = 5y
2x + y = 180
OR
2y = 5x
2x + y = 180

Solving first pair, we get
x = 75
y = 30

Solving second pair, we get
x = 100
y = 40

Hence, the remaining i.e 20, must be the answer.

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 1:38 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 14003
target 2016 - Algebra makes this harder and is not appropriate for this question.

SImple trial and improvement gets the answer in a few seconds.

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 1:48 pm

Joined: Sun Oct 19, 2014 11:52 am
Posts: 60
It's a matter of choice. There is no one way, but this way makes it show how we arrived at the answer better. Personally I don't like "trial and error"... takes me ages!

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 2:02 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 14003
As mathematicians we judge the best method as the shortest and most elegant - the choice of x and y also makes it harder to remember which variable is which. Note I said trial and improvement - not error!

e = equal angle would have been a better choice.

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 2:08 pm

Joined: Sun Oct 19, 2014 11:52 am
Posts: 60
Now that's getting pedantic. Like I said - it's a matter of choice

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 2:09 pm

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 7140
Location: East Kent
I would expect most children in y5/6 to solve it without algebra.

Agree trial and improvement, rather than error

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 Post subject: Re: isosceles trianglePosted: Sat Jan 09, 2016 2:13 pm

Joined: Sun Oct 19, 2014 11:52 am
Posts: 60
try again!

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