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DIRECTIONS for questions: Select the correct alternative from the given choices.
A rectangular piece of paper is folded in such a way that one pair of diagonally opposite vertices coincide. If the dimensions of the rectangle are 40 cm × 30 cm, what is the length (in cm) of the fold?
  • a)
    √1300
  • b)
    30√2
  • c)
    37.5
  • d)
    40
Correct answer is option 'C'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the giv...
Consider the following figure of a rectangular paper ABCD.
The line EF is the fold, which is made such that the corner D meets the diagonally opposite comer B. As DF coincides with FB upon making the fold DF = FB. Similarly, DE = EB. Also, as DF is the part of the length of the rectangle that is being folded so that D coincides with the opposite vertex and BE is the part of the length, that is being folded so that B coincides with D, DF = BE (from symmetry), i.e., quadrilateral DFBE is a rhombus (I) Now assume, FC = x cm
In the right angled triangle △BFC, BF =√BC2 + FC2 = √(30)2 + x2 = DF(since, EDBFis a rhombus and BF = DF)
Hence√302 + x2 = 40 - x
=> 900+x2= 1600 + x2– 80x
=> x = 700 / 80 = 35 / 4
Now, consider G on DC, such that EG ⊥DC. In △EGF, GF = 40 - 2x (as AE = FC = x), EG = 30 and EF is the length of the fold.
Alternative Solution
Consider the conclusion (I), i.e., that EDBF is a rhombus. Let the diagonals of the rhombus meet at O. In a rhombus, the diagonals bisect each other at right angles. Hence △EOB is similar to △DAB (both are right angled, with a common angle at B).
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DIRECTIONS for questions: Select the correct alternative from the giv...
Given:
A rectangular piece of paper with dimensions 40 cm × 30 cm.

To find:
The length of the fold when one pair of diagonally opposite vertices coincide.

Solution:
When a rectangular piece of paper is folded in such a way that one pair of diagonally opposite vertices coincide, the fold creates a right-angled triangle.

Let's consider the dimensions of the rectangle as the base and height of the triangle. The diagonal of the rectangle will be the hypotenuse of the triangle.

Step 1: Find the length of the diagonal of the rectangle using the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Using the formula, we can calculate the length of the diagonal (c) as follows:

c² = a² + b²

where a = 40 cm and b = 30 cm

c² = 40² + 30²
c² = 1600 + 900
c² = 2500
c = √2500
c = 50 cm

Step 2: Fold the rectangle in such a way that one pair of diagonally opposite vertices coincide.

When the rectangle is folded, the length of the fold will be equal to the length of the hypotenuse of the right-angled triangle formed.

Therefore, the length of the fold = 50 cm.

Conclusion:
The length of the fold when a rectangular piece of paper with dimensions 40 cm × 30 cm is folded in such a way that one pair of diagonally opposite vertices coincide is 50 cm. Hence, option C is the correct answer.
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If a line is moved through space, it traces the figure of a plane with the two dimensions of length and breadth. And, if a plane is moved in space, it traces a figure with the three dimensions of length, breadth and height.We can also work backward to form a three-dimensional body and find that the cross section of the three-dimensional cube is a two-dimensional plane, the cross section of the two-dimensional plane is a one-dimensional line and that the cross section of the line is a dimensionless point. From this, we can infer that a body of three dimensions is the cross section of a body, when moved in a certain way, of four dimensions. Then comes the question, of what sort of body could a three-dimensional shape be the cross section? 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DIRECTIONS for questions: Select the correct alternative from the given choices. A rectangular piece of paper is folded in such a way that one pair of diagonally opposite vertices coincide. If the dimensions of the rectangle are 40 cm × 30 cm, what is the length (in cm) of the fold?a) √1300b) 30√2c) 37.5d) 40Correct answer is option 'C'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the given choices. A rectangular piece of paper is folded in such a way that one pair of diagonally opposite vertices coincide. If the dimensions of the rectangle are 40 cm × 30 cm, what is the length (in cm) of the fold?a) √1300b) 30√2c) 37.5d) 40Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONS for questions: Select the correct alternative from the given choices. A rectangular piece of paper is folded in such a way that one pair of diagonally opposite vertices coincide. If the dimensions of the rectangle are 40 cm × 30 cm, what is the length (in cm) of the fold?a) √1300b) 30√2c) 37.5d) 40Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for questions: Select the correct alternative from the given choices. A rectangular piece of paper is folded in such a way that one pair of diagonally opposite vertices coincide. If the dimensions of the rectangle are 40 cm × 30 cm, what is the length (in cm) of the fold?a) √1300b) 30√2c) 37.5d) 40Correct answer is option 'C'. Can you explain this answer?.
Solutions for DIRECTIONS for questions: Select the correct alternative from the given choices. A rectangular piece of paper is folded in such a way that one pair of diagonally opposite vertices coincide. If the dimensions of the rectangle are 40 cm × 30 cm, what is the length (in cm) of the fold?a) √1300b) 30√2c) 37.5d) 40Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
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