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The perimeter of a rectangle and an equilateral triangle are same. Also, one of the sides of the rectangle is equal to the side of the triangle. The ratio of the areas of the rectangle and the triangle is
- a)√3:1
- b)1:√3
- c)2:√3
- d)4:√3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The perimeter of a rectangle and an equilateral triangle are same. Als...
Let the each side of equilateral triangle be a, then its perimeter = 3a
Again, 2(l+b)=3a
⇒ 
(for the rectangle) ⇒b=a/2
(for the rectangle) ⇒b=a/2∴ area of rectangle 
and area of triangle 
and area of triangle Most Upvoted Answer
The perimeter of a rectangle and an equilateral triangle are same. Als...
Let the side of the equilateral triangle be x. Then, the perimeter of the triangle is 3x.
Let one of the sides of the rectangle be x as well. Then, the other side of the rectangle must be (3x - 2x) = x as well (since the perimeter of the rectangle is also 3x).
Therefore, the dimensions of the rectangle are x and x, which means the area of the rectangle is x^2.
The area of an equilateral triangle with side x is (sqrt(3)/4)x^2.
So, the ratio of the areas of the rectangle and the triangle is:
x^2 / ((sqrt(3)/4)x^2) = 4/sqrt(3)
Simplifying this gives:
(4/sqrt(3)) * (sqrt(3)/sqrt(3)) = (4sqrt(3))/3
Therefore, the ratio of the areas of the rectangle and the triangle is (4sqrt(3))/3.
Let one of the sides of the rectangle be x as well. Then, the other side of the rectangle must be (3x - 2x) = x as well (since the perimeter of the rectangle is also 3x).
Therefore, the dimensions of the rectangle are x and x, which means the area of the rectangle is x^2.
The area of an equilateral triangle with side x is (sqrt(3)/4)x^2.
So, the ratio of the areas of the rectangle and the triangle is:
x^2 / ((sqrt(3)/4)x^2) = 4/sqrt(3)
Simplifying this gives:
(4/sqrt(3)) * (sqrt(3)/sqrt(3)) = (4sqrt(3))/3
Therefore, the ratio of the areas of the rectangle and the triangle is (4sqrt(3))/3.
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The perimeter of a rectangle and an equilateral triangle are same. Also, one of the sides of the rectangle is equal to the side of the triangle. The ratio of the areas of the rectangle and the triangle isa)√3:1b)1:√3c)2:√3d)4:√3Correct answer is option 'C'. Can you explain this answer?
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