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 ?

2 : $$\sqrt 3 $$
4 : $$\sqrt 3 $$
$$\sqrt 3 $$ : 2
$$\sqrt 3 $$ : 4

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Answer: Option 3

Let the side of the square be a cm Then, 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 : $$\eqalign{ & = \frac{{\sqrt 3 {a^2}}}{2}:{a^2} \cr & = \sqrt 3 :2 \cr} $$

4 views Answered 2022-09-01 13:21

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