if the length of the median of an equlilateral is x cm find its area
Answers
Hey there !
Solution:
In an equilateral triangle, the height and the median are considered to be of same length. Hence we can say that, Height of an equilateral triangle is equal to Median of the same equilateral triangle.
We know that, can be calculated as:
\text{ Height of an equilateral triangle: } = \dfrac{ \sqrt{3}}{2} a Height of an equilateral triangle: =23a
Here, 'a' denotes the side of an equilateral triangle.
\begin{gathered}\implies x = \dfrac{\sqrt{3}}{2} a \\ \\ \implies a = \dfrac{2x}{ \sqrt{3} }\end{gathered}⟹x=23a⟹a=32x
Now we know that area of an equilateral triangle can be calculated as:
\text{ Area of an Equilateral Triangle} = \dfrac{ \sqrt{3} }{4} a^2 Area of an Equilateral Triangle=43a2
Substituting the value of 'a' we get,
\begin{gathered}\implies Area = \dfrac{ \sqrt{3}}{4} \times \dfrac{2x}{ \sqrt{3}} \times \dfrac{ 2x}{\sqrt{3} } \\ \\ \implies \text{ Area} = \dfrac{ \sqrt{3} }{4} \times \dfrac{ 4x^2}{3} \\ \\ \implies \text{ Area } = \dfrac{x^2 \sqrt {3}}{3}\end{gathered}⟹Area=43×32x×32x⟹ Area=43×34x2⟹ Area =3x23
Which is the required answer !
Hope my answer helped !
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