How can I find the base of an equilateral triangle, knowing only the height?

[NickAnderson]

The question relating to this is "Assuming the height of the triangle is 1m, what is the base of the triangle to 2 decimal places?"

 

[tkhunny]

Having gloriously missed the word "equilateral" in the title, perhaps we can ignore the rest of this post. However, if you didn't really mean that, let's pay closer attention to this post.

Didn't we already do this with an isosceles triangle?

There isn't enough information. The answer is not unique. There must be something else to go on.

1) Length of congruent sides?
2) Angle at the Vertex?
3) Congruent Angles at the base?
4) Fixed area or perimeter?

What will be enough information? The height alone, and even knowing it is isosceles is simply not enough to determine a unique triangle.

 

[metastable]

The base will be a factor of (2/sqrt(3)) times longer than the height.

Square root of 3 - Wikipedia

en.m.wikipedia.org

 

[Deleted member 4993]

The question relating to this is "Assuming the height of the triangle is 1m, what is the base of the triangle to 2 decimal places?"

How can I find the base of an equilateral triangle, knowing only the height?

However, in your post you state:

The question relating to this is "Assuming the height of the triangle is 1m, what is the base of the triangle to 2 decimal places?"

No mention of equilateral triangle ! Which is it??!!

 

[pka]

No mention of equilateral triangle ! Which is it??!!

It is in the title of the thread.

 

[Steven G]

I agree that it is best to state the whole problem in the thread, not part of the problem in the title. However in my opinion the OP did state the whole problem. Sure it could have been better but it is complete.

Let x be the length of all the sides. Now draw the height. Next use Pythagoras' theorem for the left triangle you now have after drawing in the height. Solve for x.

 

[Deleted member 4993]

I agree that it is best to state the whole problem in the thread, not part of the problem in the title. However in my opinion the OP did state the whole problem. Sure it could have been better but it is complete.

Let x be the length of all the sides. Now draw the height. Next use Pythagoras' theorem for the left triangle you now have after drawing in the height. Solve for x.

My whole intention was to point out that the OP is not paying attention - S/he has no intention of "solving the problem" .

I am not "very" picky about technicality of problem statement (specially because English is NOT my vernacular and I never did get better than C in English lit.)
You state the problem is complete. It is NOT. It states:

"Assuming the height of the triangle is 1m, what is the base of the triangle to 2 decimal places." - that is an incomplete statement.

Should the answer be:

"rounded" to 2 decimal places​

​

"correct" to 2 decimal places​

Which one.......

Then of course the statement:

"... what is the base of the triangle"​

- how do you want to answer that in this question?

I want to say:

"Base is the part of the triangle which opposes the vertex" - but I don't know - how to "oppose" to 2 decimal places.

That aside, if you have noticed - we are running over each other to help an OP who has been absent during all this....