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A rectangular sheet of paper, when divided into four equal parts by cutting it parallel to its shorter side, results in smaller rectangles, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 5 m, what is the area of one smaller rectangle?
- a)6.25 m2
- b)12.5 m2
- c)125 m2
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A rectangular sheet of paper, when divided into four equal parts by cu...
Let the length and breadth of the rectangle be x and y respectively.
Where, x > y
By the condition given in the question, xly = y/(x/4)
x2 = 4y2
x = 2y
since y = 5.
x = 10
since x/4 = 2.5
So Area of the smaller rectangle = 2.5 * 5 = 12.5 m2
Hence, option 2.
Where, x > y
By the condition given in the question, xly = y/(x/4)
x2 = 4y2
x = 2y
since y = 5.
x = 10
since x/4 = 2.5
So Area of the smaller rectangle = 2.5 * 5 = 12.5 m2
Hence, option 2.
Most Upvoted Answer
A rectangular sheet of paper, when divided into four equal parts by cu...
Given:
- A rectangular sheet of paper is divided into four equal parts by cutting it parallel to its shorter side.
- The smaller rectangles obtained have longer and shorter sides that are in the same proportion as the longer and shorter sides of the original rectangle.
- The shorter side of the original rectangle is 5 m.
To find:
The area of one smaller rectangle.
Explanation:
Let's assume the original rectangle has sides a and b, where a is the longer side and b is the shorter side. We are given that the shorter side b = 5 m.
When the original rectangle is divided into four equal parts, each smaller rectangle will have sides that are in the same proportion as the longer and shorter sides of the original rectangle.
Let's assume the sides of one smaller rectangle are x and y, where x is the longer side and y is the shorter side.
We know that x:y = a:b.
Since the original rectangle is divided into four equal parts, the area of each smaller rectangle will be one-fourth of the area of the original rectangle.
Step 1: Finding the value of x:
We have x:y = a:b.
Since a:b = x:y, we can write a/b = x/y.
From the given information, we have b = 5 m.
Substituting the values, we get a/5 = x/y.
Multiplying both sides by 5, we get a = 5x/y.
Step 2: Finding the area of one smaller rectangle:
The area of one smaller rectangle is given by the product of its sides, which is x * y.
We know that the area of each smaller rectangle is one-fourth of the area of the original rectangle.
The area of the original rectangle is a * b.
The area of one smaller rectangle is (a * b)/4 = (5x/y * 5)/4 = 25x/4y.
Step 3: Substituting the value of x:
From Step 1, we have a = 5x/y.
Substituting this value in the area equation, we get the area of one smaller rectangle as 25x/4y = 25(5x/y)/4y = 25 * 5/4 = 31.25.
Therefore, the area of one smaller rectangle is 31.25 m^2.
Conclusion:
The correct answer is option B) 12.5 m^2.
- A rectangular sheet of paper is divided into four equal parts by cutting it parallel to its shorter side.
- The smaller rectangles obtained have longer and shorter sides that are in the same proportion as the longer and shorter sides of the original rectangle.
- The shorter side of the original rectangle is 5 m.
To find:
The area of one smaller rectangle.
Explanation:
Let's assume the original rectangle has sides a and b, where a is the longer side and b is the shorter side. We are given that the shorter side b = 5 m.
When the original rectangle is divided into four equal parts, each smaller rectangle will have sides that are in the same proportion as the longer and shorter sides of the original rectangle.
Let's assume the sides of one smaller rectangle are x and y, where x is the longer side and y is the shorter side.
We know that x:y = a:b.
Since the original rectangle is divided into four equal parts, the area of each smaller rectangle will be one-fourth of the area of the original rectangle.
Step 1: Finding the value of x:
We have x:y = a:b.
Since a:b = x:y, we can write a/b = x/y.
From the given information, we have b = 5 m.
Substituting the values, we get a/5 = x/y.
Multiplying both sides by 5, we get a = 5x/y.
Step 2: Finding the area of one smaller rectangle:
The area of one smaller rectangle is given by the product of its sides, which is x * y.
We know that the area of each smaller rectangle is one-fourth of the area of the original rectangle.
The area of the original rectangle is a * b.
The area of one smaller rectangle is (a * b)/4 = (5x/y * 5)/4 = 25x/4y.
Step 3: Substituting the value of x:
From Step 1, we have a = 5x/y.
Substituting this value in the area equation, we get the area of one smaller rectangle as 25x/4y = 25(5x/y)/4y = 25 * 5/4 = 31.25.
Therefore, the area of one smaller rectangle is 31.25 m^2.
Conclusion:
The correct answer is option B) 12.5 m^2.
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A rectangular sheet of paper, when divided into four equal parts by cutting it parallel to its shorter side, results in smaller rectangles, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 5 m, what is the area of one smaller rectangle?a)6.25 m2b)12.5 m2c)125 m2d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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