Altitude of an equilateral triangle with perimeter of 48 cm?

Question

Help please!

Answer 1

Each side is 16cm. The altitude can be found by using the pythagorean theorem. c = 16, a = 8. a^2 + b^2 = c^2

Answer 2

It is always true that the length of the altitude of an equilateral triangle is x√3/2 where x=length of a side.

48/3=16 cm for the length of any one of the sides

altitude=16√3/2=8√3 cm

 

If you want to do it out the long way...

The altitude forms a right triangle (actually two right triangles) with the hypotenuse equal to 16, the altitude is "a", and the other leg is (1/2)(16) or 8.

Using the Pythagorean Theorem...

16^2=8^2+a^2

256=64+a^2

256-64=a^2

a^2=192

√a^2=√192

√a^2=√64*3

a=8√3 cm