The side of an equilateral ?ABC is 7cm. Find the side of another equilateral ?PQR whose area is 3times the area of ?ABC.

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Solution

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$A r e a o f t r i a n g l e A B C = \frac{\sqrt{3}}{4} a^{2} = \frac{\sqrt{3}}{4} {(7)}^{2} = \frac{49 \sqrt{3}}{4} c m^{2} L e t t h e s i d e o f t r i a n g l e P Q R b e b c m I t i s g i v e n t h a t a r e a o f T r i a n g l e P Q R = 3 \times A r e a o f t r i a n g l e A B C \Rightarrow \frac{\sqrt{3}}{4} (b^{2}) = 3 \times \frac{49 \sqrt{3}}{4} \Rightarrow b^{2} = 147 \Leftrightarrow b = \sqrt{147} \Rightarrow b = 7 \sqrt{3} c m S o, t h e s i d e o f t h e t r i a n g l e P Q R i s 7 \sqrt{3} c m .$
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