The perimeter of triangle MNO is 30 cm. MP bisects angle M. Find MN and MO.

Apples+Pears^2

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Screenshot 2021-02-16 at 11.54.10 AM.png
Perimeter is 30 cm, MP bisects angle M, and I have to find MN and MO.
All I have so far is :
(Let y be MN and let x be MO)
3/7 = y/x (set up as a proportion)
3x = 7y
and,
3 + 7 + x + y = 30
x + y = 20

I'm not really sure how to solve this and if anyone could help that would be great, thanks!
 

Dr.Peterson

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3x = 7y
x + y = 20
This is a system of equations; in fact, they are linear equations, so you have probably learned a couple ways to solve it. Try substitution.
 

AmandasMathHelp

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Why did you set up proportions? These triangles are not simular so I don't see how proportions apply to those sides.
 

Dr.Peterson

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Why did you set up proportions? These triangles are not similar so I don't see how proportions apply to those sides.
There is a theorem that justifies this step.

And the picture is very inaccurate; to scale, it looks more like this:
1613524887890.png
 
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Apples+Pears^2

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Oh ok that makes sense. I got the answer now. Thank you everyone! :)
 

Dr.Peterson

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Since you've solved it, I'll tell you how I immediately did it in my head.

The perimeter is 30, so the sum of the unknown sides has to be 20. They have to be in the ratio 3:7. Since 3+7 = 10, we just have to double everything.
 

Apples+Pears^2

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Since you've solved it, I'll tell you how I immediately did it in my head.

The perimeter is 30, so the sum of the unknown sides has to be 20. They have to be in the ratio 3:7. Since 3+7 = 10, we just have to double everything.
OHHHHH~ I see how that works now.
For MN I got 6 and MO I got 14. And it works, since 6 is double of 3 and 14 is double of 7 and all the sides added together for perimeter is 30. :)
Thank you! =)
 
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