Find the perimeter of an equlaterial triangle w/ hight of 7sqroot 3?

Question

All sides are equal so all sides must be 7sqroot3?
If so, add all up?

10points for the correct anwser

Answer 1

The height isn't the side length, it's the altitude to the base.

For an equilateral triangle, the altitude splits the triangle in half, where each half is a 30-60-90 triangle. In that half-triangle, the hypotenuse is one side of the equilateral triangle, the short leg is half of another side of the equilateral triangle, and the longer leg is the altitude (which is 7sqrt(3)).

A 30-60-90 triangle has side lengths in ratio 1:sqrt(3):2, so if the altitude (the sqrt(3) ratio) has length 7sqrt(3), then the hypotenuse (one side) has length 2/sqrt(3) times as big.

7sqrt(3) * 2/sqrt(3) = 14

So... if an equilateral triangle has height 7sqrt(3), then each side of the equilateral triangle is length 14.

This means that the perimeter is 3*14 = 42.

Answer 2

The height is 7sqrt(3), but the height is not a side.

You can use Pythagoras's Theorem to calculate a side, because you know that all sides are equal. Let x be the length of a side, then:
(7sqrt(3))² + (x/2)² = x²
147 + (x/2)² = x²
x² - (x/2)² = 147
x² - x²/4 = 147
x² (1-1/4) = 147
x² = 147/(3/4)
x² = 196
x = sqrt(196)
x = 14

Therefore, the perimeter is 3(14) = 42

Answer 3

Heh, this is one of those cases where the wise-@$$ Douglas Adams fans would be correct.

Anyway, the height is NOT a side of the triangle. That only works for right triangles. The height here is the line that comes down from the top corner and is perpendicular to the base.

When you draw this line, it splits up the triangle into two 30-60-90 triangles. Mark the angles of one of these smaller triangles. Notice that sin(60) = (height) / (one of the sides), so sqrt(3)/2 = 7sqrt(3) / side, and the length of one side of the original triangle is therefore 14. This means the perimeter is 3*14 = 42 units.

Answer 4

No. If the height is 7 sqrt(3), the sides are each 14, and the perimeter is 42. Show this by dropping a perpendicular from any corner to the other side; this line will be a bisector, and the resulting right triangle solved with Pythagoras.

Answer 5

No.
The height is 7sqrt(3).
If a side has length x, then:
(x/2) / 7sqrt(3) = tan(30) = 1 / sqrt(3)
x / 14sqrt(3) = 1 / sqrt(3)
x = 14.
The perimeter is 3 * 14 = 42.

Answer 6

Let sides = x
sin 60° = h / x
x = h / sin 60°
x = 7.√3 / √3 / 2
x = 14
Perimeter = 42

Answer 7

42

Answer 8

21 sqrt 3 is your answer. Hope I helped. Peace.

Answer 9

its 21sqrt 3
you add the base and the sqrt stays the same.