Find the exact value for the perimeter of an equilateral triangle with an altitude of 18 cm

9514 1404 393

  36√3 cm

Step-by-step explanation:

The perimeter of an equilateral triangle is 2√3 times the height.

  P = (2√3)h

  P = (2√3)(18 cm) = 36√3 cm

A little more detail

The hypotenuse of a 30°-60°-90° triangle is 2/√3 times the longer leg. Here, the longer leg is 18 cm, so the side length of the equilateral triangle is ...

  18(2/√3) = 12√3 . . . cm

The equilateral triangle perimeter is 3 times that, or 36√3 cm.

step-by-step explanation:

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