If the altitude of an equilateral triangle is 10 cm, find the perimeter.?

Question

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Answer 1

side = 20/sqrt(3)
Perimeter = 60/sqrt(3) = 20 sqrt(3)

Answer 2

If you don't know trigonometry you can use the pythagorean theorem. Let x be the length of a side. The altitude splits the triangle into two right triangles with legs 10 cm and x/2 cm long and hypotenuse x cm long, so

(x/2)^2 + 10^2 = x^2

You can solve this for x; the perimeter is then 3x.

Answer 3

The altitude effectively creates a third side for a 30-60-90 angled triangle. Therefore 10 divided by the squareroot of 3 would be half of one side of the equilateral triangle. Multiply that by 6 and you get 60 divided by the squareroot of 3. Simply multiply by the square root of 3 to both the top and bottom (special form of 1) and you get 20 root 3.

Answer 4

uncomplicated formulation for the climate of a ideal triangle is a^2 + b^2 = c^2 all of us understand that a = 10. we additionally understand that c = 2b because of the fact the triangle is equilateral. one hundred + b^2 = 4b^2 one hundred = 3 b^2 b^2 = one hundred / 3 so b = the sq. root of one hundred / 3 the fringe would be 6b additionally 30º-60º-90º Triangles yet another style of particular ideal triangles is the 30°- 60°- ninety° triangle. that's perfect triangle whose angles are 30°, 60°and ninety°. In a 30°-60°-ninety° triangle the climate are interior the ratio a million : 2 : and the sq. root of three

Answer 5

A good way to do this is to picture your triangle split in two in the middle. Leaving you two identical 10cm high triangles.

then sin60/sin90=10/x x=11.547
since every side is equal the perimeter=11.547*3=34.64
which is equal to 20*sqrt(3)

Answer 6

let x be the half of base of the triangle
tan60=10/x
x=10/tan60
the total base length is 20/tan60=11.54
the total perimeter is 60tan60=34.64cm.