The diagonal of a square is twice the side of equilateral triangle then the ratio of Area of the ...
The diagonal of a square is twice the side of equilateral triangle then the ratio of Area of the Triangle to the Area of Square is?
Answer/Solution
3√8
Steps/Work
Let the side of equilateral triangle = 1 unit.
We know that area of an equilateral triangle = 3–√4a234a2
As side = 1 unit area of the equilateral triangle = 3–√434
Now Diagonal of the square = 2 (side of the equilateral triangle) = 2
We know that area of the square = 12D212D2 where D = diagonal
So area of the square = 12(22)=212(22)=2
Ratio of the areas of equilateral triangle and square = 3–√434 : 2 ⇒⇒ 3√8
Answer:B
We know that area of an equilateral triangle = 3–√4a234a2
As side = 1 unit area of the equilateral triangle = 3–√434
Now Diagonal of the square = 2 (side of the equilateral triangle) = 2
We know that area of the square = 12D212D2 where D = diagonal
So area of the square = 12(22)=212(22)=2
Ratio of the areas of equilateral triangle and square = 3–√434 : 2 ⇒⇒ 3√8
Answer:B