Find the altitude of an equilateral triangle whose perimeter is 18

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Find the altitude of an equilateral triangle whose perimeter is 18

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Thiên Di 4 years 2021-07-22T22:09:32+00:00 1 Answers 13 views 0

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  1. thienan
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    2021-07-22T22:11:28+00:00
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    Answer:

    3√3 units

    Step-by-step explanation:

    We are asked to find the altitude of the equilateral triangle whose perimeter is 18 . Firstly let us find the side of the∆.

    \rm \implies a + a + a = 18 \\\\\rm\implies 3a = 18 \\\\\rm\implies a = 6

    Now we know that in a equilateral triangle , the altitude of the triangle with side length a is ,

    \rm\implies Altitude =\dfrac{\sqrt3}{2} a

    Plug in the value of a that is 6 , we will get ,

    \rm\implies Altitude =\dfrac{\sqrt 3}{2} a \\\\\rm\implies Altitude =\dfrac{ \sqrt3}{2}\times 6 \\\\\rm\implies Altitude = \sqrt3 \times 3 \\\\\rm\implies\boxed{ \bf Altitude = 3\sqrt3 \ units }

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