Math Help. Triangles?

Question

An Equilateral triangle has an area of 30. What is its perimeter?

please help.

Answer 1

Let "x" be the length of one side of the triangle. Label each side of the triangle "x".

If you split an equilateral triangle down the middle (thus marking the triangle's height), it splits the triangle into two 30-60-90 triangles where the hypotenuse is one side of the triangle. Half of the triangle's base is just x/2. Using the properties of 30-60-90 triangles, the height is (x/2)*√3. So the area of the triangle is
(x/2)(x/2)√3.

This has to equal thirty, so set it equal to 30 and solve for x:

(x/2)(x/2)√3 = 30
(x²)√3 = 30*4
(x²) = 120/√3
(x²) = 120*√3/3
(x²) = 40√3
x = √(40√3)
x = 2√(10√3)

The perimeter is then 3x, or 6√(10√3), which is about 24.97

Answer 2

The perimeter's length is 24.9707... . Here's how it's found :

Let each side be of length b --- including the base, naturally.

The area of a triangle is (1/2) b h, where ' h ' is the height. For such a triangle, the height is sqrt(3) b / 2, so the area is:

[sqrt(3) b^2] / 4 = 30 (as given). Therefore

b^2 = 4 x 30 / sqrt(3) = 69.2820..., or b = 8.3236...

The perimeter = 3 b = 24.9707... .

Live long and prosper.

Answer 3

Let the side be a. Then the perpendicular height is (a/2)sqrt(3).
Area is = (a^2)sqrt(3)/4 = 30. This gives a = 8.324. Perimeter = 3 x 8.324 = 24.972

Answer 4

In Equaliteral triangle all sides are equal.
Let the side be "x".
Area of triangle = (sqrt(3)/4)*x*x
Perimeter of triangle = 3x.
30 = (sqrt(3)/4)*x*x
X = 8.324
Perimeter = 3x
= 3 (8.324)
= 24.97 =` 25.

Answer 5

The area for the triangle:
A=1/2bh

√3(b^2)/4=30
b^2=(30*4)/√3
b^2=69.282.........
b=8.324
3(8.324)=24.971

Answer 6

Sorry dude, can't do your homework here.