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

Question

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

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Huyền Thanh 4 years 2021-08-17T14:10:30+00:00 1 Answers 12 views 0

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  1. niczorrrr
    0
    2021-08-17T14:11:31+00:00
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    9514 1404 393

    Answer:

      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.

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