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