anonymous
  • anonymous
How would I solve the area? The base of the triangle is 25 and dotted ling is 10cm.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
is the dotted line in the middle of the triangle? is the triangle equilateral?
SolomonZelman
  • SolomonZelman
|dw:1450404923702:dw|
SolomonZelman
  • SolomonZelman
|dw:1450405029041:dw|

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SolomonZelman
  • SolomonZelman
Do you agree with this?
SolomonZelman
  • SolomonZelman
(Taking the difference of those triangles (lower left and the entire left) - to find the area of the upper left triangle.)
anonymous
  • anonymous
yeah so i do same thing to other side just double the area
SolomonZelman
  • SolomonZelman
We will see if the x will be a factor in your answer, then you understand that this left WILL impact the area.
SolomonZelman
  • SolomonZelman
and if x goes away (cancels), then information is correct and we didn't need to know this length,.
anonymous
  • anonymous
so this comes out to a specific number?
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
So, let's do the math for the area of the triangles.
SolomonZelman
  • SolomonZelman
again , ...
SolomonZelman
  • SolomonZelman
|dw:1450405314870:dw|
SolomonZelman
  • SolomonZelman
so that triangle is a(10+x)/2 - ax/2 (1/2)(10a+ax-ax) (1/2)(10a)
SolomonZelman
  • SolomonZelman
then same for|dw:1450405389696:dw|
SolomonZelman
  • SolomonZelman
you do the same exact thing but your "a" is 25-a.
anonymous
  • anonymous
ok but why not just say the base is 12.5 on each half?
SolomonZelman
  • SolomonZelman
We don't know if they are equal. Therefore I intorduced "a"...
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
(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)
SolomonZelman
  • SolomonZelman
|dw:1450405551543:dw|
SolomonZelman
  • SolomonZelman
now, we will add the areas.
SolomonZelman
  • SolomonZelman
5(25-a)+5a 125-5a+5a 125
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
if you have questions, ask.
anonymous
  • anonymous
what type of triangle is this called or is there a name?
SolomonZelman
  • SolomonZelman
are you taking about the whole shape?
SolomonZelman
  • SolomonZelman
or one triangle within the shape?
anonymous
  • anonymous
yeah because i don't recognize ever seeing this type of problem before
SolomonZelman
  • SolomonZelman
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...
SolomonZelman
  • SolomonZelman
|dw:1450405862331:dw|
SolomonZelman
  • SolomonZelman
|dw:1450405888292:dw|
SolomonZelman
  • SolomonZelman
and the sum of upper triangles does NOT change... (as we clarified... and if you don't understand why, then ask me)
SolomonZelman
  • SolomonZelman
((I am not really a mathematician [yet], I am just a guy and I am applying my logic to the problem. ))
anonymous
  • anonymous
I appreciate your help thank you very much for taking the time to clarify more meaning for me:)
SolomonZelman
  • SolomonZelman
so, you don't have any questions regarding this....
SolomonZelman
  • SolomonZelman
YW
anonymous
  • anonymous
well my problem is starting out how to attack such problems...
anonymous
  • anonymous
once you stated take top half and subtract bottom half, I can visually see what your doing now
SolomonZelman
  • SolomonZelman
|dw:1450406628210:dw|
SolomonZelman
  • SolomonZelman
Normally the area of the triangle is base•height÷2, right?
SolomonZelman
  • SolomonZelman
But you are not really given any of this information...
SolomonZelman
  • SolomonZelman
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...
SolomonZelman
  • SolomonZelman
then I just did the areas of the triangle.
SolomonZelman
  • SolomonZelman
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?
anonymous
  • anonymous
I have a hard time with geometry because I don't see what is the right way to start solving such a problem
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
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.

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