Question

The value median of an equilateral triangle is x cm. What is the value of its area?​

Answer 1

Step-by-step explanation:

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: =

2

3

a

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=

2

3

a

⟹a=

3

2x

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=

4

3

a

2

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=

4

3

×

3

2x

×

3

2x

⟹ Area=

4

3

×

3

4x

2

⟹ Area =

3

x

2

3

Answer 2

Answer:

above answer is correct