If the area of an equilateral triangle is 36√3 cm^2 find the height​

1 thought on “If the area of an equilateral triangle is 36√3 cm^2 find the height​”

1. Given:-

   • Area of the Equilateral Triangle = 36√3cm²

   To Find:-

   • Height of an equilateral triangle.

   Formula Used:-

   • [tex]{\boxed{\bf{Area\:of\: Equilateral\: Triangle=\dfrac{\sqrt{3}}{4}a^2}}}[/tex]

   • [tex]{\boxed{\bf{Height\:of\: Equilateral\:Triangle=\dfrac{\sqrt{3}}{2}a}}}[/tex]

   Solution:-

   Firstly,

   [tex]\sf :\implies\:Area=\dfrac{\sqrt{3}}{4}a^2[/tex]

   [tex]\sf :\implies\:36\sqrt{3}=\dfrac{\sqrt{3}}{4}a^2[/tex]

   [tex]\sf :\implies\:a^2=36\times4[/tex]

   [tex]\sf :\implies\:a^2=144[/tex]

   [tex]\sf :\implies\:a=\sqrt{144}[/tex]

   [tex]\bf :\implies\:a=12\:cm[/tex]

   Now,

   [tex]\sf :\implies\: Height=\dfrac{\sqrt{3}}{2}a[/tex]

   [tex]\sf :\implies\: Height=\dfrac{\sqrt{3}}{2}\times12[/tex]

   [tex]\bf :\implies\: Height=6\sqrt{3}\:cm[/tex]

   Hence, The Height of the Equilateral triangle is 6√3 cm.

   ━━━━━━━━━━━━━━━━━━━━━━━━━

   Reply