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Instead of walking along two adjacent sides of a rectangular field,a boy took shortcut along the diagonal and saved a distance equal to the half of the longer side.then the ratio of shorter side of the rectangular field to its longer side is.? a)4:3 b)3:4 c)3:2 d)2:3 Correct answer is "b".can u explain this?
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Instead of walking along two adjacent sides of a rectangular field,a b...
Let x be the shorter side and y be the longer one. The shortcut route would be of length \sqrt{x^2+y^2}
x 2 +y 2
According to given condition we know that (x+y)- \sqrt{x^2+y^2}
x 2+y 2
= y/2 . Solving, we get 1=(x/y)+(1/4)
=> x : y = 3 : 4. Hence option B is the correct answer.
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Instead of walking along two adjacent sides of a rectangular field,a b...
Explanation:
The key to solving this problem lies in understanding the geometry of the situation and applying the concepts of distance and ratios.
Given Information:
- The boy took a shortcut along the diagonal of the rectangular field.
- He saved a distance equal to half of the longer side by taking this shortcut.
Understanding the Problem:
- Let the shorter side of the rectangular field be 'x' units.
- Let the longer side of the rectangular field be 'y' units.
Distance Saved:
- The boy saved a distance equal to half of the longer side by taking the diagonal shortcut.
- This means, the distance of the diagonal = y/2.
Using Pythagoras Theorem:
- In a rectangle, the diagonal divides the rectangle into two right-angled triangles.
- Using Pythagoras Theorem, we can write: x^2 + y^2 = (y/2)^2.
Solving the Equation:
- Substituting x^2 + y^2 = (y/2)^2 into the Pythagoras equation, we get:
- x^2 + y^2 = y^2/4.
- Simplifying, we get: x^2 = 3y^2/4.
Ratio of Shorter Side to Longer Side:
- Taking the square root on both sides, we get: x = √(3y^2)/2.
- Simplifying, we get: x = (√3 * y)/2.
- Therefore, the ratio of the shorter side to the longer side is 3:4.
Therefore, the correct answer is option (b) 3:4.
The key to solving this problem lies in understanding the geometry of the situation and applying the concepts of distance and ratios.
Given Information:
- The boy took a shortcut along the diagonal of the rectangular field.
- He saved a distance equal to half of the longer side by taking this shortcut.
Understanding the Problem:
- Let the shorter side of the rectangular field be 'x' units.
- Let the longer side of the rectangular field be 'y' units.
Distance Saved:
- The boy saved a distance equal to half of the longer side by taking the diagonal shortcut.
- This means, the distance of the diagonal = y/2.
Using Pythagoras Theorem:
- In a rectangle, the diagonal divides the rectangle into two right-angled triangles.
- Using Pythagoras Theorem, we can write: x^2 + y^2 = (y/2)^2.
Solving the Equation:
- Substituting x^2 + y^2 = (y/2)^2 into the Pythagoras equation, we get:
- x^2 + y^2 = y^2/4.
- Simplifying, we get: x^2 = 3y^2/4.
Ratio of Shorter Side to Longer Side:
- Taking the square root on both sides, we get: x = √(3y^2)/2.
- Simplifying, we get: x = (√3 * y)/2.
- Therefore, the ratio of the shorter side to the longer side is 3:4.
Therefore, the correct answer is option (b) 3:4.
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Instead of walking along two adjacent sides of a rectangular field,a boy took shortcut along the diagonal and saved a distance equal to the half of the longer side.then the ratio of shorter side of the rectangular field to its longer side is.? a)4:3 b)3:4 c)3:2 d)2:3 Correct answer is "b".can u explain this?
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Instead of walking along two adjacent sides of a rectangular field,a boy took shortcut along the diagonal and saved a distance equal to the half of the longer side.then the ratio of shorter side of the rectangular field to its longer side is.? a)4:3 b)3:4 c)3:2 d)2:3 Correct answer is "b".can u explain this? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Instead of walking along two adjacent sides of a rectangular field,a boy took shortcut along the diagonal and saved a distance equal to the half of the longer side.then the ratio of shorter side of the rectangular field to its longer side is.? a)4:3 b)3:4 c)3:2 d)2:3 Correct answer is "b".can u explain this? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Instead of walking along two adjacent sides of a rectangular field,a boy took shortcut along the diagonal and saved a distance equal to the half of the longer side.then the ratio of shorter side of the rectangular field to its longer side is.? a)4:3 b)3:4 c)3:2 d)2:3 Correct answer is "b".can u explain this?.
Instead of walking along two adjacent sides of a rectangular field,a boy took shortcut along the diagonal and saved a distance equal to the half of the longer side.then the ratio of shorter side of the rectangular field to its longer side is.? a)4:3 b)3:4 c)3:2 d)2:3 Correct answer is "b".can u explain this? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Instead of walking along two adjacent sides of a rectangular field,a boy took shortcut along the diagonal and saved a distance equal to the half of the longer side.then the ratio of shorter side of the rectangular field to its longer side is.? a)4:3 b)3:4 c)3:2 d)2:3 Correct answer is "b".can u explain this? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Instead of walking along two adjacent sides of a rectangular field,a boy took shortcut along the diagonal and saved a distance equal to the half of the longer side.then the ratio of shorter side of the rectangular field to its longer side is.? a)4:3 b)3:4 c)3:2 d)2:3 Correct answer is "b".can u explain this?.
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