Hello math bugs(🐞) and hivers (🐝)
I hope you are strong and stout & doing good in life.
Well come back to another interesting geometric concept. It is Mass Point Geometry. Check the problem below. It is very difficult to solve the problem if you don't know Mass Point Geometry. The concept itself is very easy but the using it to solve a problem may be challenging if you are not familiar with it. Before heading to the solution , I want to give you a insight about the concept. I'll request you give it a try before checking the concept or the solution.
BALANCING WEIGHT:
We have seen it in Grocery shop , in meat shop and in vegetables shop. The Rod or pole is balanced parallel to the ground. Both side of the pole are of same length from middle to both end.We use weight on one side and on the other side things we wanna measure. As we can see it in the following figure.
Have you ever thought what happen if the pole or Rod is not balanced before starting measurement. I mean if the pole is not 1:1 ratio, how should we get a correct measurement. The concept is simple we have to know one thing that The ratio of length of the rod must be inverse of the weight of both sides. Check it in the following figure. If we do so, the pole will always be parallel to the ground.
The concept discussed above must be very simple to you.Yeah it is really simple. Now we need to know how to use it in geometry. Check today's problem has a lot of pole in the from of line segment. We gonna use above concept considering the line segment as a pole or a rod.
Let me mention all the concepts that need to solve the problem:
✅ Ratio of area of triangle is same as ratio of bases if the height is the same.
✅ Mass Point geometry discussed above.
✅ Knowledge of ratio and it's equivalent ratio.
It's time to face the problem figure 👩🔧
Let's find the ratio of BO and DO. If height is the same , ratio of area becomes the ratio of bases. Check it below:
Let's make sum of two terms of the two ratios obtained above equal to make the calculation easier.Check it in the figure below:
Now It's time to use Mass Point geometry concept. Let me remind you once again ratio of weight on the both end must be the same as ratio of the pole or Rod from the hanging point.
Consider both BD and AE as pole or Rod of a common balance of measurement. Total weight on the both side can also be considered in the middle as done in the following figure.
In the previous and following frames, area of triangle and their bases are equaled because their heights are the same.
The process may seem a bit hard if you are doing it for the first time. But once you got the idea how Mass Point geometry cane be use, it can be solved orally.
I hope you like today's concept.If you have any query ,please feel free to ask for. If you find any silly mistake , please ignore it. All the frame I used took time and re-editing is not possible. I am sorry for that.😂😂
Thanks for visiting and supporting
Have a good day
Regards: meta007