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is the dotted line in the middle of the triangle? is the triangle equilateral?
Do you agree with this?
(Taking the difference of those triangles (lower left and the entire left) - to find the area of the upper left triangle.)
yeah so i do same thing to other side just double the area
We will see if the x will be a factor in your answer, then you understand that this left WILL impact the area.
and if x goes away (cancels), then information is correct and we didn't need to know this length,.
so this comes out to a specific number?
If x goes away, then we don't need to know the length which I denoted by x. If x doesn't go away, then we will say that there isn't a numerical solution, because then the length denoted by x will impact the area.
So, let's do the math for the area of the triangles.
again , ...
so that triangle is a(10+x)/2 - ax/2 (1/2)(10a+ax-ax) (1/2)(10a)
then same for|dw:1450405389696:dw|
you do the same exact thing but your "a" is 25-a.
ok but why not just say the base is 12.5 on each half?
We don't know if they are equal. Therefore I intorduced "a"...
if "a" cancels, then if sides are equal wouldn't matter, but if "a" doesn't cancel then the equivalences of sides, and how different they are does play a role.
(1/2)(10a) is same as 5a. And for the right side instead of "a" you do say but with "25-a" instead of a. 5(25-a)
now, we will add the areas.
5(25-a)+5a 125-5a+5a 125
And yes, it turns out that the difference of horizontal sides, and the length denoted by x, don't matter for the SUM of the area of upper triangles.
if you have questions, ask.
what type of triangle is this called or is there a name?
are you taking about the whole shape?
or one triangle within the shape?
yeah because i don't recognize ever seeing this type of problem before
Well, this is rather a critical thinking problem. You are given only 2 parameters, and they want you to solve this regarding "x" and "a" (which as I showed "x" and "a" don't matter and thus problem has numerical solution). The whole triangle is not called anything, and I will draw you why...
and the sum of upper triangles does NOT change... (as we clarified... and if you don't understand why, then ask me)
((I am not really a mathematician [yet], I am just a guy and I am applying my logic to the problem. ))
I appreciate your help thank you very much for taking the time to clarify more meaning for me:)
so, you don't have any questions regarding this....
well my problem is starting out how to attack such problems...
once you stated take top half and subtract bottom half, I can visually see what your doing now
Normally the area of the triangle is base•height÷2, right?
But you are not really given any of this information...
So I thought that I will denote everything (as I did), and if the parameters "a" and "x" dissapear from the problem then numerical solution exists, if those don't go away then no numerical solution...
then I just did the areas of the triangle.
But your question was this, OR was it - how did I come up with the idea of subtracting bottom-left triangle from the entire-left triangle?
I have a hard time with geometry because I don't see what is the right way to start solving such a problem
That is very likely going to go away with practice... or perhaps you just need to be taught and everything explained with logic rather than "this is the formula" and "for example you apply it here", WITHOUT "why this is the formula" and "why you apply it here" the why's do exist, but they are weak, and that is the problem for most math-students.
For example, I don't know the formula for, say, differentiation a polar function, but I know the calculus and I can logically derive the formula in my head in it's entirety... logic rules, and not (necessarily) the knowledge.