1. The diagonal of a square equals the side of an equilateral triangle. If the area of the square is 6√3 sq cm, what is the area of the equilateral triangle?
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By: anil on 05 May 2019 02.13 am
Let the side of square = $$s$$ cm and diagonal = $$d$$ cm => Area of square = $$(s)^2 = 6sqrt{3}$$ ----------(i) In right triangle of the square, => $$(s)^2 + (s)^2 = (d)^2$$ Substituting value of $$s^2$$ from equation (i) => $$(d)^2 = 6sqrt{3} + 6sqrt{3} = 12sqrt{3}$$ ----------(ii) Side of equilateral triangle = Diagonal of square = $$d$$ cm $$ herefore$$ Area of equilateral triangle = $$frac{sqrt{3}}{4} d^2$$ Substituting value of $$d^2$$ from (ii), we get : = $$frac{sqrt{3}}{4} imes 12sqrt{3} = frac{36}{4} = 9 cm^2$$ => Ans - (B)
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