If the altitude of an equilateral triangle is #8sqrt3#, what is the perimeter of the triangle?

Answer 1

The altitude of an equilateral triangle is the perpendicular line from a vertex to the opposite side.

This always forms a 30, 60, 90 triangle with the two triangles that form. (Try to prove this for "fun" Hint: HL = HL and CPCTC)

What do we know about 30-60-90 triangles? We know the relationship between angles and side lengths!

Since the altitude is opposite the 60 degree angle, the altitude is equal to #xsqrt3#.
Therefore, we can set #8sqrt3 = xsqrt3#
Clearly, #x = 8#
Since the side opposite the 30 degree angle is x, the other leg length would be #8#
Finally, we know that the hypotenuse is 2x, so the length would be #16#

We are trying to find the perimeter; we know that one side is 16.

Alas, it is an equilateral triangle, so all of the sides are length 16.

So we just add the lengths up, #16 + 16+16 = 48#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7