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If the area of a square is equal to the area of that rectangle whose width is double of the one side of the square then the ratio of the length to the breadth of the rectangle will be?
- a)1 : 2
- b)1 : 4
- c)1 : 6
- d)1 : 8
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the area of a square is equal to the area of that rectangle whose w...
b = 2a
a = b/2
Area of square = b²/4 = Area of rectangle
l * b = b²/4 ⇒ l = b/4
l / b =(b/4)/b ⇒ 1:4
a = b/2
Area of square = b²/4 = Area of rectangle
l * b = b²/4 ⇒ l = b/4
l / b =(b/4)/b ⇒ 1:4
Most Upvoted Answer
If the area of a square is equal to the area of that rectangle whose w...
To solve this problem, let's assume that the side of the square is 'x'. According to the question, the area of the square is equal to the area of the rectangle, whose width is double the side of the square.
1. Area of the square:
The area of a square is given by the formula A = side^2. So, the area of the square is x^2.
2. Area of the rectangle:
The width of the rectangle is double the side of the square, so it is 2x. The length of the rectangle is not given, so let's assume it to be 'y'. Therefore, the area of the rectangle is given by the formula A = length * width. Substituting the values, we get A = y * 2x.
3. Equating the areas:
According to the question, the area of the square is equal to the area of the rectangle. So, we have x^2 = y * 2x.
4. Simplifying the equation:
Dividing both sides of the equation by x, we get x = 2y.
5. Ratio of length to breadth:
The ratio of length to breadth is given by the formula length/breadth. Substituting the values, we have y/x = y/(2y). Simplifying further, we get 1/2.
Therefore, the ratio of length to breadth of the rectangle is 1:2, which is option 'B'.
1. Area of the square:
The area of a square is given by the formula A = side^2. So, the area of the square is x^2.
2. Area of the rectangle:
The width of the rectangle is double the side of the square, so it is 2x. The length of the rectangle is not given, so let's assume it to be 'y'. Therefore, the area of the rectangle is given by the formula A = length * width. Substituting the values, we get A = y * 2x.
3. Equating the areas:
According to the question, the area of the square is equal to the area of the rectangle. So, we have x^2 = y * 2x.
4. Simplifying the equation:
Dividing both sides of the equation by x, we get x = 2y.
5. Ratio of length to breadth:
The ratio of length to breadth is given by the formula length/breadth. Substituting the values, we have y/x = y/(2y). Simplifying further, we get 1/2.
Therefore, the ratio of length to breadth of the rectangle is 1:2, which is option 'B'.
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If the area of a square is equal to the area of that rectangle whose width is double of the one side of the square then the ratio of the length to the breadth of the rectangle will be?a)1 : 2b)1 : 4c)1 : 6d)1 : 8e)None of the AboveCorrect answer is option 'B'. Can you explain this answer?
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