An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square ?
A. 2 : $$\sqrt 3 $$
B. 4 : $$\sqrt 3 $$
C. $$\sqrt 3 $$ : 2
D. $$\sqrt 3 $$ : 4
Answer: Option C
Solution(By Examveda Team)
Let the side of the square be a cmThen, the length of its diagonal = $$\sqrt 2 $$ a cm
Area of equilateral triangle with side :
$$\eqalign{ & = \sqrt 2 a \cr & = \frac{{\sqrt 3 }}{4} \times {\left( {\sqrt 2 a} \right)^2} \cr & = \frac{{\sqrt 3 {a^2}}}{2} \cr} $$
∴ Required ratio :
$$\eqalign{ & = \frac{{\sqrt 3 {a^2}}}{2}:{a^2} \cr & = \sqrt 3 :2 \cr} $$
Related Questions on Area
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D. 307200 m2
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The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
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B. 42%
C. 44%
D. 46%
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