Question 59
The side of an equilateral triangle is equal to the diagonal of the square. If the side of the square is 10 cm, then what is the area of the equilateral triangle?
Solution
Side of square = 10 cm
=> Diagonal of square = $$\sqrt{(10)^2+(10)^2}$$
= $$\sqrt{200}=10\sqrt2$$ cm
Thus, side of equilateral triangle = $$10\sqrt2$$ cm
$$\therefore$$ Area of equilateral triangle = $$\frac{\sqrt3}{4} (a)^2$$
= $$\frac{\sqrt3}{4}\times(10\sqrt2)^2$$
= $$\frac{\sqrt3}{4}\times200=50\sqrt3$$ $$cm^2$$
=> Ans - (B)
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