Question

An equilateral triangle has an area of 50 units 2. What is the length of each side?

Answer 1

• Length of each side of equilateral Traingle is 10.75 units

Explanation:

Given that area of an equilateral traingle 50 square units.

Let the length of side of equilateral traingle be 'x' units. To calculate length of each side we will use the formula of area of equilateral traingle:

`\: \: { \underline { \boxed{\pmb { \sf{ \purple {Area_((equilateral \: traingle)) = (\sqrt 3)/(4) * (Side)^2}} }}}} \\`

By substituting the values in above formula:

`~`

`: \implies \sf \: \: 50 = ( √(3) )/(4) * {(x)}^(2) \\ \\ \\ : \implies \sf \: \: {(x)}^(2) = (50 * 4)/( √(3) ) \\ \\ \\ : \implies \sf \: \: {(x)}^(2) = (200)/( √(3) ) \\ \\ \\ : \implies \sf \: \: x = \sqrt{ (200)/( √(3) ) } \\ \\ \\ : \implies \: \: { \boxed{\pmb{ \frak{ x = 10.75 \: units }}}}\\ \\ \\`

• Hence, Length of each side of equilateral Traingle is 10.75 units