If a side of a equilateral triangle is 3, why cant we use the pythagorean theorem

MERRY CHRISTMAS BTW!

Law of cosines.

The Pythagorean theorem is a special case of the more general theorem relating the lengths of sides in any triangle, the law of cosines.

a^2 + b^2 - 2ab cos(theta) = c^2

Where theta is the angle between sides a and b.

When theta is 90 degrees, then cos(theta) = 0, and the formula reduces to the usual Pythagorean theorem.

That can only be used for right triangles. Right triangles have a right angle at one vertex btw, merry christmas to you too! lol

Idk why the 3 is necessary. I'm assuming you're asking for math schoolwork, so I guess they want you to use it to explain why not. Plug the sides into the pythagorean equation.

a^2+b^2=c^2
3^2+3^2=3^2
Solve: 9+9=9
Since 18 doesn't equal 9, there is no solution, and you have proved that the pythagorean theorem cannot be used with an equilaterla triangle with side length 3.

If you draw perpendicular from vertex then to find altitude u can use pythagorean theorem
(h)^2 + (3/2)^2 = 3^2
h^2 = 9 -9/4 = 27/4
h = sqrt(27)/2
h= (3/2)sqrt(3) .......................Ans
Area = (1/2)(3/2){sqrt(3)}
= (3/4) sqrt(3) .................Ans

Pythagoras theorem only works with right angled triangles. An equilateral is not a right angle triangle as each angle in an equilateral triangle is 60 degrees no matter what the length of a side is.

Pyathagorous theorem is used only for right angeled triangles