Question

The area of an equilateral triangle is numerically equal to its perimeter. Find the length of its sides, correct two decimal places.

Answer 1

Let each side of an equilateral triangle measures a cm.
Then, we have

`sqrt(3)/(4) xx "a"^2` = a + a + a

⇒ `sqrt(3)/(4) xx "a"^2` = 3a

⇒ `"a"^2/"a" = (4)/sqrt(3) xx 3`

⇒ a = `4sqrt(3)`
⇒ a = 4 x 1.732
⇒ a = 6.928
⇒ a = 6.93 units.