Question

if each side of an equilaterel triangle is doubled then its area becomes how many times​

Answer 1

Answer :

4 times

Step-by-step explanation :

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

Let the side of the equilateral triangle be "a units"

AB = BC = CA = a units

Area of the equilateral triangle

       $\sf =\dfrac{\sqrt{3}}{4} a^2$

Now, each side of the equilateral triangle is doubled

 a' = 2a units

New area :

  $\sf =\dfrac{\sqrt{3}}{4} a'^2 \\\\ \sf =\dfrac{\sqrt{3}}{4} (2a)^2 \\\\ \sf =\dfrac{\sqrt{3}}{4} \times 4a^2 \\\\ \sf = 4 \bigg(\dfrac{\sqrt{3}}{4} a^2 \bigg)$

Therefore, It's area becomes 4 times if each side of the equilateral triangle is doubled.

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Equilateral triangle :

• All sides are equal.
• Each angle is 60°

• Height  $\sf =\dfrac{\sqrt{3}}{2} a$

where 'a' is the side