Given GE=x, ET=4x, EA=16, find perimeter, area of triangle AGT

happiness

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I don't know how to start, I think 16 = geometric mean of 4x+x. Help me find the perimeter and area idk how to even start the problem.
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Typically a good place to start with problems like these is just to write down every piece of information you're given and then see what else you can deduce. For instance, you might note that triangle AEG is a right triangle. What does that tell you about the length of AG? Also note that the larger triangle GAT is also a right triangle. What does that tell you about the length of AT? Using this new information, what, then, can you say about the perimeter of the triangle? What can you say about the area of the triangle? With only the information given, I don't see any way to determine a numerical value of either the perimeter or the area, but you can definitely create an expression for both, in terms of x.
 
I don't know how to start, I think 16 = geometric mean of 4x+x. Help me find the perimeter and area idk how to even start the problem.

You've made a great start; just continue!

Write an equation stating that 16 = geometric mean of 4x and x. Solve that for x.

Then let Pythagoras find the other sides for you. Perimeter and area follow easily.
 
Find area and perimeter

I think the small triangle(GEA) is a 60,30 special right triangle. Again stuck on how to find the side AT because 4x won't work with Pythagorean Theorem. Please some assistance.

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I think the small triangle(GEA) is a 60,30 special right triangle. Again stuck on how to find the side AT because 4x won't work with Pythagorean Theorem. Please some assistance.

Isn't this the same problem I offered help with at https://www.freemathhelp.com/forum/threads/111176-Find-the-perimeter-and-area?p=428649#post428649 ? Why haven't you taken that advice?

But why have you changed the 16 to 16√3?? In fact, it looks like you also wrote in the right angles; were you told that separately?

Either way, it is not 30-60-90; a guess won't work. Please show actual work.
 
(The two threads have been merged.)

Note: It looks to me as though the right angles have been pencilled in. This is not information which was given, but which was assumed. As such, I don't think it can be used, can it?
 
Yes I did pencil in the extra information, it was not given. I penciled in that information because I assumed it was a 60,30 special right triangle.
 
The point is that the "tick marks" on the legs of the triangle is a standard way of indicating that they are congruent. This is an isosceles right triangle with angles 45-45-90, not 30-60-90.
 
Yes I did pencil in the extra information, it was not given. I penciled in that information because I assumed it was a 60,30 special right triangle.

Without assuming the two right angles (or something similar), this problem can't be solved.

You should never be expected to assume something from the appearance of a picture; this is a bad problem. But I suspect that is what they did, and you are supposed to take those as right angles; that's why I suggested you might have been told it.

On the other hand, assuming that is far more reasonable than assuming an angle is 60 degrees, even when it looks like it. It is typical for figures in problems to be "not to scale", meaning that angles can't be trusted.

(By the way, your work on problem 7 is wrong. I see that you identified the longest side, but I'd expect to see a corollary of the Pythagorean theorem used. I have no idea what the left side is, or why you would think they were equal.)
 
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