Finding the Area of ABMN: A Geometry Problem

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The discussion revolves around finding the area of the quadrilateral ABMN within a rectangle ABCD, where M is the midpoint of BC and N is the intersection of lines AC and MD. Participants suggest calculating the areas of triangles MCB and ABC using the lengths of AB and BC, labeling them as x and y for clarity. The challenge lies in determining the height of triangle MNC, which can be approached by establishing a coordinate system and solving linear equations for the intersecting lines. The final area ratio mentioned is 2:5, indicating a specific relationship in the areas involved. The conversation briefly diverges into unrelated topics, but the primary focus remains on solving the geometry problem.
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In the figure, ABCD is a rectangle. M is the midpoint of BC and AC intersects MD at N.
Find the Area of the NCD: Area of ABMN.

I am sorry i don't know how to solve this question. Thanks.
 

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Well you can find areas of MCB and ABC easy enough in terms of lengths AB and BC (I'm assuming your answer neads to be in terms of AB and BC-so I would label them x and y to make it easier) Then the only trick would be finding the area of MNC, you can find the base easy enough the height is the tricky part. Once you know the area of MNC finding NCB and ABMN should be simple.

As far as finding the height of MNC I might try creating a coordinate system for the figure then finding linear equations for the lines AC and MD then solving the two equations simultaneously to find their point of intersection.
 
In fact, the ans is 2:5. And I can calculate this question by using your method. Thank.
 
Your welcome. And that's true for any rectangle? How interesting.
 
tamalkuila said:
prove that primes of the form 4n+1 are infinite?send the proof to tamalkuila@gmail.com
What does this have to do with the original question?

The Bob (2004 ©)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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