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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.
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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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