An equilateral triangle of side $4\sqrt[4]{3}cm$ formed out of a sheet is converted into a rectangle such that there is no loss of the area of the triangle. Then the least perimeter of the rectangle (in cm) will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $8\sqrt{3}$
Area = $\frac{\sqrt{3}}{4}.side^2$
$=\frac{\sqrt{3}}{4}(4\sqrt[4]{3})^2$
$=\frac{\sqrt{3}}{4}.16\sqrt{3}$
$=12cm^2$
To minimize the perimeter the rectangle should be as clost to a square as possible.
Let $l=b$
$l.b=12⇒l^2=12$
$⇒l=2\sqrt{3}cm$
∴ The perimeter = $4l=8\sqrt{3}cm$